Electric Current

 ELECTRIC CURRENT :

If electric charges such as electrons, ions, charged particles flows we say that there exist an electric current.

Consider a cell is connected to a torch bulb through metallic wires and a switch. On switching on the circuit, electric current is produced which flow through the wire and filament of the torch bulb, heat it up and the filament begins to glow.

Here in this case, electrons starts flowing when the cell was connected to the torch bulb through wires and switch. This flow of electrons in the metallic wire constitute the electric current.

Definition OF Electric Current: 
Electric current is defined as the rate of flow of charge flowing through a cross-section of a wire/conductor. 

Formula: If a net charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is 

\[I = \frac{Q}{t}\]

SI Unit :
The SI unit of electric charge is coulomb (C) and time is second (s). Thus the SI unit of electric current is coulomb/second (C/s). This unit is given a special name called ampere (A), named after the French scientist, Andre-Marie Ampere (1775–1836). 

Definition of 1 ampere :

One ampere is that amount of current when an electric charge of one coulomb flows through a cross section of wire in one second. That is, 

\[1A=\frac{1C}{1s}\]

Small units of electric current: 

Small quantities of current are expressed in 
(i) milliampere

\[1mA=10^{-3}A\]

(ii) microampere

\[μA=10^{-6}A\]

Device used to measure current :

An instrument called ammeter measures electric current in a circuit. 

Symbol:

Connection in circuit: 

It is always connected in series in a circuit through which the current is to be measured. 

The Red terminal (positive terminal) is connected to the positive terminal of the battery and black terminal (negative terminal) is connected to the negative of the battery.

Direction of electric current :
Conventionally, in an electric circuit the direction of electric current is taken as opposite to the direction of the flow of electrons, which are negative charges. In an electric circuit electric current flows from the positive terminal of the cell to the negative terminal of the cell through the bulb and ammeter.


Electric circuit :
A continuous and closed path of an electric current is called an electric circuit.

Electric switch :
A switch makes a conducting link between the cell and the bulb. If the switch of the circuit is turned off, the current stops flowing and the bulb does not glow. 
Charge of an electron: 

\[1.6 \times 10^{-19}C\]

Number of electrons in 1C of charge: 

\[6.25 \times 10^{18}\]

NOW CHECK YOUR PROGRESS!!! 

1. What does an electric circuit mean? 
2. Define the unit of current. 
3. Calculate the number of electrons constituting one coulomb of charge. 
4. A current of 0.5 A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of charge that flows through the circuit. 
5. Name the instrument used to measure electric current in a circuit. How is this instrument connected in a circuit? Draw a simple circuit diagram to explain your answer. 
6. Which particles constitute electric current in a metallic conductor? 
7. Name two units for expressing the small values of current. Also write their symbols. How are these units related to ampere? 
8. Write the use of following components in an electric circuit 
(a) Cell/battery 
(b) Ammeter 
(c) Connecting wires 
(d) Switch/plug key 

Working of electric motor

ELECTRIC MOTOR

An electric motor is a rotating device which converts electrical energy into mechanical energy.
It means it takes energy from electricity and using this energy the motor system rotates its rotator. The motion of rotator means that it possesses mechanical energy.
It appears so simple but we have to understand the process by which this energy change take place.

Image Credit -Lookang many thanks to Fu-Kwun Hwang and author of Easy Java Simulation = Francisco Esquembre, Ejs Open Source Direct Current Electrical Motor Model Java Applet ( DC Motor ) 20 degree split ring, CC BY-SA 3.0

The basic principle behind the working of motor is that when a current carrying wire is placed in a magnetic field it experiences a force. The direction of this force can be determined by Fleming’s left hand rule.

Thus using electrical energy we setup an electric current in a coil
and in an electromagnet. The electromagnet thus behaves like a magnet. The current carrying coil when placed in magnetic field of electromagnet experiences a force. Using suitable arrangement and designing, the coil can be made to rotate.

Construction
A simple electric motor consists of a rectangular coil ABCD of insulated copper wire placed between two opposite poles magnets as shown in the figure. The ends of the coil are connected to two half of a split ring (S1 and S2) attached to the axle. The split rings are connected to two carbon brushes B1 and B2 as shown in the figure. The carbon brushes are connected to a battery through connecting wire and a key (or switch).

©Udvita.org

Working:
First Half Cycle

Let the plane of coil is initially placed horizontally as shown in the figure. The direction of current in the coil is along ABCD. The direction of magnetic field is from North pole to the south pole.
By applying Fleming’s left hand rule on arm AB, the direction of force on arm AB is downward. Similarly the direction of force on arm CD is upward. Under the action of two equal and opposite will make the coil mounted on an axle to rotate anticlockwise.

Second Half Cycle
After half a rotation, arms AB and CD will interchange its position. The split ring S1 is now in contact with brush B2 and the split ring S2 is in contact with brush B1. The direction of current in the coil is now DCBA, reversed as compared to first half cycle. A device which reverses the direction of current in a circuit is called commutator. In electric motor, split rings acts as commutator.

©Udvita.org

By applying Fleming’s left hand rule on arm AB, the direction of force on arm AB is upward. Similarly the direction of force on arm CD is downward. Again under the action of two equal and opposite will make the coil mounted on an axle to rotate anticlockwise.

Commercial motor
A commercial motor consists of an electromagnet instead of permanent magnets. The current carrying coil consists of a large number of turns (in thousands). A soft iron core is used on which the coil is wound.
The soft iron core along with the coil is called the armature.

Image credit-Abnormaal, Electric motor, CC BY-SA 3.0

Uses of electric motor
Electric motor is used in electric fans, water pumps, mixer, MP3 player, computer etc

Simplest Electric Motor
Watch the Simplest electric Motor video made by our YouTube Channel partner 'Learn n hv Fun'.
The motor is simply made using a copper coil and few neudymium magnets using a 1.5V  electric cell.

Question of the day 15 Nov 2107

Question of the day 15 Nov 2017

A student has two resistors A and B of resistance 4 ohm and 6 ohm respectively.  The student was challenged by the Physics teacher to connect them to a 12 V battery so as to draw maximum current from the voltage source.

How would you advice the student to connect the resistors and what would be the current obtained?

Question of the day 14/11/2017

Question of the day - 14 Nov 2017

The resistance of an electric heating device is 20 ohms. If an electric current of 5 A flows through the device for 30 seconds. Determine

(i) Potential difference applied across the device.

(ii) heat produced in the device in 30 seconds.

The Story of Electricity

THE STORY OF ELECTRICITY

Imagine a world without any electricity. Imagine your home now… no televisions, no air conditioners, no light, no refrigerator, no machines, no mobile phones, no electronic gadgets to assist you, no apps, no facebook, no twitter… The only form of electricity available to us would be that of lightning.

Ohh.. what a boring life…

But life would be very close to nature. Sun and fire will be the only source of light. Watching birds, animals would be your favorite pass time. Crude handmade gadgets like magnetic compass, hammer, knife would be your apps. Pigeon would serve as twitter, FB…

So my dear friend, electricity is an integral part of our modern life. The study of electricity is necessary so that such a vast knowledge is not lost overtime. It must be passed to the next generation.

I am doing my duty as I am passing the story to electricity to you..

Take a piece of copper metal. If you view the copper at the microscopic level you would find a lot of empty space with copper atoms suspended in space in the cloud of electrons. Most of the electrons in the cloud are orbiting to some copper atoms or the other. Some electrons in the cloud are wandering from one atom to the other, colliding with other atoms and electrons. At this microscopic level, everything happens very fast. Electrons are moving at 10⁶m/s, atoms are vibrating very rapidly with a frequency of ……..

Suddenly, in the macroscopic, outer world, a human connected the metal plate to a battery.

In the inner atomic world, there is a change in the scene now. The cloud of wandering electrons  start moving towards positive terminal of the battery with a very slow speed of 1mm/s. The number of wandering electrons are however enormous. About 10²² in few grams of copper.

We call this flow of electrons as electric current.

When such moving electrons are made of pass through a filament of electric bulb, it heats up to approx 2700°C and starts glowing. 

This is how we use electricity of light a bulb.

Watch the video from YouTube to understand electricity in a more detail.

Ohm's Law

Ohm's Law is a relationship between potential difference applied across a conductor to the electric current flowing in it.

You must have experienced the following situations in daily life:

(1) Fluctuations in voltage which leads to dimming or brightening of electric bulb. (This is the reason why we use stabilizers for ACs - to prevent any damage due to voltage fluctuations ) 
(2)  While playing with LEDs, torch bulb, electric cells and connecting wires you must have observed that by increasing the number of cells in the circuit the LEDs glows brighter.
(3) A 12V battery provides a large amount of current than a 3V battery.

This suggests that there must be a relation between voltage (potential difference) and electric current. This relationship is known as Ohm's Law.

Ohm's law was given by George Simon Ohm in the year 1827. This is a relation between potential difference (V) applied across the ends of a conductor to the electric current (I) flowing in the conductor

According the Ohm's Law, the electric current flowing in a conductor is directly proportional to the potential difference (V) applied across the ends of a conductor provided the temperature of the wire remains the constant.

Mathematically,
                              I    ∝    V
or it can also be written as

                            V  ∝    I
removing the proportionality sign and introducing a constant

                            V   =  R I

Where R is a constant known as the resistance of the given conductor.

Graph:

The V–I graph is a straight line that passes through the origin of the graph, as shown in Figure. Thus,
\[\frac{V}{I}\]
is a constant ratio.

Resistance

Physically, resistance is defined as a property of a conductor to resist the flow of charge through it.

The SI unit of resistance is ohm (Ω)  (Greek symbol omega)

A conductor is said to have a resistance of 1Ω when a potential difference of 1V is applied across the ends of a conductor and a current of 1A flows through it.
\[R=\frac{V}{I}\]
\[1Ω=\frac{1V}{1A}\]

A fan regulator is actually a variable resistor. It changes the resistance of the circuit and thereby we can control the speed of the fan.

To test your knowledge on Ohm's Law, attempt the following test.

you will get your score immediately. 

Click the link below to attempt the test:

Online Test on Ohm's Law

Some more questions on Ohm's Law:

1. Name and state the law which relates the current in a conductor to the potential difference across a conductor and the current flowing through it.

2. Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?

3. When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.


4. (a) How much current will an electric bulb draw from a 220 V source, if the resistance of the bulb filament is 1200 Ω? (b) How much current will an electric heater coil draw from a 220 V source, if the resistance of the heater coil is 100 Ω?

5. The potential difference between the terminals of an electric heater is 60 V when it draws a current of 4A from the source. What current will the heater draw if the potential difference is increased to 120 V?

6. The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below –
I (amperes) 0.5    1.0     2.0      3.0       4.0
V (volts)     1.6    3.4     6.7     10.2     13.2
Plot a graph between V and I and calculate the resistance of that resistor.

7. Keeping the potential difference constant, the resistance of a circuit is doubled. By how much does the current change?

QUESTION OF THE DAY 09/05/2015

Question of the day September 9, 2015

Three electric lamps A, B and C are rated as follows:

Lamp A : 40 W, 220 V

Lamp B: 60 W, 220 V and

Lamp C: 100 W, 220 V

Which lamp has higher resistance? Give reason.

Question Bank Electricity

A Question Bank provides you a plenty of good questions for practice and meaningful discussion with your peers. It saves time and make you confident in the subject. The following is the Question Bank on Electricity Class 10 standard.

1.    What does an electric circuit mean?

2.    Define the unit of current.

3.    Calculate the number of electrons constituting one coulomb of charge.

4.    A current of 0.5 A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of charge that flows through the circuit. (Ans. 300 C)

5.    Name the instrument used to measure electric current in a circuit. How is this instrument connected in a circuit? Draw a simple circuit diagram to explain your answer.

6.    Which particles constitute electric current in a metallic conductor?

7.    Name two units for expressing the small values of current. Also write their symbols. How are these units related to ampere?

8.    Name a device that helps to maintain potential difference across a conductor.

9.    What is meant by saying that potential difference between two points is 1V?

10.   Write the relation which states the relation between potential difference and work done.

11.   How much energy is given to each coulomb of charge passing through a 6V battery?

12.   How much work is done in moving a charge of 2 C across two points having a potential difference of 12 V?

13.   Name the device that measures the potential difference across two points in an electric circuit. How it is connected in an electric circuit?

14.   Name and state the law which relates the current in a conductor to the potential difference across a conductor and the current flowing through it.

15.   Define the SI unit of resistance.

16.   (a) How much current will an electric bulb draw from a 220 V source, if the resistance of the bulb filament is 1200 Ω? (Ans. 0.183 A)

        (b) How much current will an electric heater coil draw from a 220 V source, if the resistance of the heater coil is 100 Ω? (Ans. 2.2 A)

17.   The potential difference between the terminals of an electric heater is 60 V when it draws a current of 4 A from the source. What current will the heater draw if the potential difference is increased to 120 V? (Ans. 8 A)

18.   A wire of given material having length l and area of cross-section A has a resistance of 4 Ω. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A? (Ans. 1 Ω)

19.   On what factors does the resistance of a conductor depend?

20.   Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?

21.   Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?

22.   Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?

23.   When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor. (Ans. 4800Ω)

24.   Why is the tungsten used almost exclusively for filament of electric lamps?

25.   Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?

26.   How does the resistance of a wire vary with its area of cross-section?

27.   Why copper and aluminium wires are usually employed for electricity transmission?

28.   Keeping the potential difference constant, the resistance of a circuit is doubled. By how much does the current change?

29.   Give two examples of materials which are (i) good conductor (ii) resistor (iii) insulator (iv) poor conductor.

30.   Why do electricians wear rubber hand-gloves while working with electricity?

31.   Name the device used to change resistance in a circuit to regulate current without changing the voltage source.

32.   What is nichrome? State its one property and one use.

33.   Define resistivity. What is its SI unit? On what factor does it depends?

34.   A wire of resistance 20 Ω is stretched to double its length. What will be its new (i) resistivity (ii) resistance? (Ans. New R = 80 Ω)

35.   The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below –

                    I (amperes)    0.5     1.0      2.0      3.0      4.0


                    V (volts)       1.6       3.4      6.7     10.2     13.2

Plot a graph between V and I and calculate the resistance of that resistor.

36.   Write the use of following components in an electric circuit
        (a) Cell/battery
        (b) Ammeter
        (c) Connecting wires
        (d) Switch/plug key

37.   A wire of resistance R is cut into five equal pieces. These five pieces of wire are then connected in parallel. If the resultant resistance of this combination be R then the ratio of resultant to the original will be?

38.   A radio set draws a current of 0.36 A for 15 minutes. Calculate the amount of electric charge that flows through the circuit. (Ans. 324 C)

39.   Potential difference between two points of a wire carrying 2 ampere current is 0.1 volt. Calculate the resistance between these points. (Ans. 0.05Ω)

40.   A simple electric circuit has a 24 V battery and a resistor of 60 ohms. What will be the current in the circuit? The resistance of the connecting wires is negligible. (Ans. 0.4 Ω)

41.   Find resistance between A and B in following network

42.   A resistance of 6 ohms is connected in series with another resistance of 4 ohms. A potential difference of 20 volts is applied across the combination. Calculate the current through the circuit and potential difference across the 6 ohm resistance. (Ans. 2 A, 12 V)

43.   Calculate the work done in moving a charge of 5 Coulombs from a point at a potential of 210 Volts to another point at 240 Volts. (Ans. 150 J)

44.   How many electrons pass through a lamp in one minute if the current be 200 mA? (72 x 10^18)

45.   Calculate the current supplied by a cell if the amount of charge passing through the cell in 4 seconds is 12 C ? (Ans. 4 A)

46.   A 2 Volt cell is connected to a 1 Ω resistor. How many electrons come out of the negative terminal of the cell in 2 minutes? (Ans. 1440 x 10^18)

47.   A torch bulb when cold has 1Ω resistance. It draws a current of 0.3 Ampere when glowing from a source of 3 V. Calculate the resistance of the bulb when glowing and explain the reason for the difference in resistance. (Ans. 10Ω)

48.   A current of 0.2 Ampere flows through a conductor of resistance 4.5 Ω. Calculate the potential difference at the ends of the conductor. (Ans. 0.9 V)

49.   You have two metallic wires of resistances 6 ohm and 3 ohm. How will you connect these wires to get the effective resistance of 2 ohm?

50.   State Ohm’s law. “The resistance of a conductor is 1Ω.” What is meant by this statement?

51.   Prove that 1 J is equivalent to 1 Vx A x s.

52.   How long does it take a current of 5.0 mA to deliver 15 C of charge? (Ans. 3000 s)

53.   What is the potential difference between two points if 1.0 kJ of work is required to move 0.5 C of charge between the two points? (Ans. 2000 V)

54.   What is the voltage of a source which provides 12.0 J to each Coulomb of charge present?

55.   What is the potential difference between two points when a charge of 80.0 C has 4.0 x 10^3J of energy supplied to it as it moves between the two points? (Ans. 50 V)

56.   There is a current of 0.50 A through an incandescent lamp for 5.0 min, with a voltage of 115 V. How much energy does the current transfer to the lamp? What is the power rating of the lamp? (Ans. 17250 J, 57.5 W)

57.   If there is a current of 2.0 A through a hair dryer transferring 11 kJ of energy in 55 s, what is the potential difference across the dryer? (Ans. 100 V)

58.   An electric drill operates at a potential difference of 120V and draws a current of 6.0 mA. If it takes 40 s for the drill to make a hole in a piece of wood, how much energy is used by the drill? (Ans. 28.8 J)

59.   An electric toaster operating at a potential difference of 115 V uses 3220 J of energy during the 20 sec it is on. What is the current through the toaster? (Ans. 1.4 A)

60.   A motor draws a current of 2.0 A for 20.0 sec in order to lift a small mass of 500 g. If the motor does a total of 9.6 kJ of work calculate the voltage drop across the motor. (Ans. 240 V)

61.   In a lightning discharge, 30.0 C of charge moves through a potential difference 108 V in 20 minute. Calculate the current of the lightning bolt. (Ans. 0.025 A)

62.   How much energy is gained by an electron accelerated through a potential difference of 3.0 x 10^2 V? (4.8 x 10­-17 J)

63.   A 12V car battery can provide 6 A for 1.0 h. how much energy is stored in the battery? (Ans. 259200 J)

64.   a) Describe the difference between current in a series circuit and current in a parallel circuit.
        b) Describe the difference between voltage in a series circuit and voltage in a parallel circuit.

65.   Draw a schematic diagram of the following circuit: One power source and a resistor are connected in series with a combination of 3 light bulbs connected in parallel with each other. Include a fuse, 4 switches, a voltmeter, and an ammeter. The fuse should protect the whole circuit, one switch should shut off the whole circuit and the other switches should control the individual bulbs. The ammeter should read current drawn from power source and the voltmeter the voltage of the resistor.

66.   Describe the effect on the rest of the bulbs in the above problem when one burns out. Will the remainder glow brighter or dimmer? What will be the effect on the source?

67.   a) What is a short circuit? b) Why is it dangerous? c) Give two ways to protect against short circuits.

68.   A conductor has a length of 2.0 m and a radius of 3.0 mm. If the resistance is R = 100 Ω, calculate the new resistance if the same material has:
        a) length = 6.0 m and r = 6.0 mm (Ans. 75 Ω)
        b) length = 1.0 m and r = 1.0 mm (Ans. 450 Ω)

69.   List two ways to increase the current drawn by a circuit.

70.   A voltmeter measures a voltage drop of 60.0 V across a heating element while an ammeter reads the current through it as 2.0 A. What is the resistance of the heating coil? (Ans. 30Ω)

71.   How much current flows through a 7.5 W light bulb with a potential difference of 1.5 V? (Ans. 5A)

72.   A set of 6 identical motors are connected in series to a 120 V source drawing 1.0 A of current. Find:
       a) R total
       b) R of each motor
       c) Voltage drop across each load. (Ans. 120Ω, 20Ω and 20 V)

73.   A set of 6 identical motors are connected in parallel to a 150 V source drawing 1.2 A of current. Find:
        a) R total
        b) R of each motor
        c) Current through each motor
        d) Voltage drop across each load. (Ans. 125Ω, 750Ω, 0.2 A and 150 V)

74.   Do resistors in parallel increase or decrease total resistance?

75.   What resistance must be added in series to a circuit containing a 45 ohm resistor in order to draw 2.0 A of current from a 120V source? (Ans. 15 Ω)

76.   What makes the electric charge to flow?

77.   The V–I graph is a straight line that passes through the origin of the graph. What do you conclude from this observation?

78.   Define the commercial unit of energy. Relate it to joules.

79.   Discuss the activity to show that resistance of a conductor depends on its length and area of cross section.

80.   Which common factor affects both resistance as well as resistivity?

81.   Alloys are commonly used in electrical heating devices. Why?

82.   It is impracticable to connect an electric bulb and an electric heater in series. Why?

83.   What is heating effect of electric current? Name the various devices in which this effect is utilized.

84.   State the Joule’s law of heating. Derive the expression for the same.

85.   Which effect of current is responsible for the glow of an electric bulb? Explain.

86.   The bulbs are usually filled with few gases. Name those gases. Also discuss the cause for the same.

87.   Which metal is used as the filament of an electric bulb and why?

88.   How does a fuse work in the electric circuit?

89.   Which materials are preferred for a fuse wire and why?

90.   Give the ratings of various fuses used in the domestic circuit.

91.   A torch bulb is rated at 3V and 600mA. Calculate it’s a) Power b) Resistance c) Energy consumed if it is lighted for 4 Hrs. (Ans. 1.8 W, 5 Ω, 0.0072kWh/25920 J)

92.   Which will offer more resistance a 50W lamp or 25W lamp bulb and how many times? (ans. 25 W, 2 times)

93.   Why should the heating element of an electric iron be made of iron, silver or Nichrome wire?

94.   If a wire is stretched to triple its original length, what happens to its resistivity?

95.   Two identical resistors each of resistance 10 ohm are connected 1) in series 2) in parallel, in line to a battery of 6volts. Calculate the ratio of power consumed in the combination of resistors in the two cases. (Ans. 1:4)

96. A bulb is rated at 220V- 100W. What is its resistance? Five such bulbs burn for 4 hrs. What is the energy consumed? Calculate the cost if the rate is Rs. 5 per unit? (Ans. 484 Ω 2kWh, Rs 10)

97.   Two lamps rated 100W, 220V and 120W, 220V are connected in parallel to 220V supply. Calculate the total current through the circuit. (Ans. 1 A)

98.   How does the resistance of wire change when 1) Its length is doubled 2) Area is doubled?

99.   A wire of resistance 10ohm is bent in the form of a closed circle. What is the effective resistance between the two points at the end of any diameter of the circle? (Ans. 2.5 Ω)

100.  When resistances are connected in series, which physical quantity remains constant?

101.  When resistances are connected in parallel, which physical quantity remains constant?

102.  Resistance of an incandescent filament of lamp is more than that when it is at the room temperature. Why?

103.  The length of a wire is doubled and its cross sectional area is also doubled. What is the change in its (i) resistivity (ii) resistance?

104.  Name two characteristics of a heating element wire.

105.  For an electric iron of 1kW rating at 220V, fuse of how much capacity is to be used? (Ans. 5A)

106.  What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?

107.  How can three resistors of resistances 2Ω, 3Ω and 6Ω be connected to give a total resistance of (a) 4Ω (b) 1Ω ?

108.  Why does the cord of an electric heater not glow while the heating element does?

109.  Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50V. (Ans. 4800 kJ)

110.  An electric iron of resistance 20 Ω takes a current of 5A. Calculate the heat developed in 30 s. (Ans. 15 kJ)

111.  What determines the rate at which energy is delivered by current?

112.  An electric motor takes 5A from a 220 V line. Determine the power of the motor and the energy consumed in 2 hours. (Ans. 1.1 kW, 2.2 kWh)

113.  A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then obtain the ratio of .

114.  An electric bulb is rated 220 V and 100 W. What will be the power consumed when it is operated on 110 V ? (Ans. 25 W)

115.

V-I graph for two conductors A and B obeying Ohm’s law is given in figure 4. Which conductor has more resistance?

116.

V-I graph for parallel and series combination of two metallic resistors is shown as in figure 5. Which graph represents the parallel combination? Justify your answer.

117.  Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then connected in parallel in a circuit across the same potential difference. Obtain the ratio of heat produced in series and parallel combination. (Ans. 1:4)

118.  How many 176 Ω resistors in parallel are required to carry 5 A on a 220 V line? (Ans.4 resistors)

119.  Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A? (Ans. 110 bulbs)

120.  Compare the power used in the 2Ω resistor in each of the following circuits:
        (i) a 6 V battery in series with 1Ω and 2Ω resistors, and
        (ii) a 6 V battery in parallel with 12 Ω and 2Ω resistors. (Ans. 8W, 18 W)

121.  Which uses more energy, a 250 W TV set in 1 hour, or a 1200 W toaster in 10 minutes?

122.  An electric heater of resistance 8Ω draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater. (Ans. 1800 W)

123.  (i) State the formula showing how the current I in a conductor varies when the potential difference V applied across it is increased stepwise.
        (ii) Show this relationship on a schematic graph.
        (iii) Calculate the resistance of a conductor if the current flowing it is 0.2 A, when the applied potential difference is 0.8V.

124.  A torch bulb is rated 2.5 V and 750 mA. Calculate 
         (i) its power, 
         (ii) its resistance, and 
         (iii) the energy consumed if this bulb is lighted for 4 hours.                                                 (Ans. 1.875 W, 3.3Ω, 0.0075kWh)

125.  A wire of resistance 4Ω is doubled on it. Calculate the new resistance of the wire. (Ans. 1Ω)


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Domestic Electric Circuit

Domestic Electric Circuit

1.     Household electric supply consists of 3 types of wire. Live wire (red insulation cover), neutral wire (black insulation cover) and earth wire (green insulation cover)

2.    The potential difference between neutral and live wire is 220V.

3.    In household circuit system, two type of circuit are used. One of 15 A for appliances with higher power ratings and the other of 5 A ratings for bulbs etc.

4.    In domestic circuit, different appliances are connected in parallel combination. This ensures that if one appliance is switched ‘on’ or ‘off’, the others are not affected.

5.    The earth wire is used as a safety measure, especially for those appliances that have a metallic body.

Working of earth wire 

The metallic body is connected to the earth wire, which provides a low resistance-conducting path for the current. It ensures that any leakage of current to the metallic body of the appliance will flow to the earth only and the user may not get a severe shock.
Watch the video below to more explanation on working of earth wire.

Short circuit

It means that the two wires live and neutral have come in contact with each other. This may happen either due to their insulation have been damaged or due to a fault in the appliance. In such a case, the resistance of the circuit decreases to a very small value. According to Ohm’s law, the current increases enormously. It may results in spark at the place of short circuit, which may even cause fire. Sometimes, the current also increase due to overloading of the circuit.

Overloading

It is a situation when too many appliances are connected in the same circuit such that the overall current (sum of all the current used by all appliances) exceeds the current carrying capacity of the connecting wires. The wires cannot withstand such a high current and melt and may cause fire. 

The electric fuse

Electric fuse is used as safety device for the protection of electric circuits and appliances due to short circuiting or overloading of the circuit.. The electric fuse is a piece of wire having a very low melting point and high resistance.When a high current flows through the circuit due to short circuit or overloading, the fuse wire gets heated and melts. The circuit is broken and current stops flowing thus save the electric circuit and appliance form damage.

Capacities of fuse wire

The fuse for domestic purposes are rated as 1A, 2A, 3A, 5A, 10A and 15A.         

Characteristics of fuse wire

1.    Low melting point
2.    High resistance 

Fuse wire are made up of pure tin or made of an alloy of copper and tin.              

AC and DC

Alternating Current and Direct Current

Alternating Current (AC)

It is a current whose magnitude changes continuously and direction changes periodically.

The source of AC is AC generator.

In India mostly current is supplied in AC form. The frequency of AC in India is 50 Hz. It means AC changes direction every 1/100 of a second. In complete cycle of AC, it changes its direction twice.

Direct Current (DC)

It is a current whose magnitude is always constant and such a current flows in one direction only.

The source of DC are DC generators, cells, batteries etc

Advantage of AC over DC

1.  An alternating current (AC) can be transmitted to long distances without much power loss where as if direct current (DC) is supplied to long distance that most of its energy is wasted in the form of Joule’s heat.

2.  An alternating current (AC) can be step-up and step-down i.e. the voltage can be increased or decreased with the help of transformers whereas a DC can not step-up or step-down.

Electric power

Expression for work done:

\[W=VIt\]

\[W=I^2Rt\]

\[W=\frac{V^2t}{R}\]

ELECTRIC POWER 

Electrical power is the rate at which electric energy is dissipated or consumed in an electric circuit. 

The power P is given by
\[P=\frac{W}{t}\;\;\text{ or  } \;\;P=\frac{E}{t}\]
\[P=VI\]
\[P=I^2R\]
\[P=\frac{V^2}{R}\]

SI Unit:

 The SI unit of electric power is watt (W). 

Definition of 1 watt: 

It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus, 

1 W = 1 volt × 1 ampere = 1 V A 

Bigger unit of power:

(a) kilowatt (kW)

         1 kW = 1000 W

(b) Megawatt (MW)

          1 MW = 1000 kW = 1000000 W = \(10^6\) W

Watt-hour 

Watt-hour (Wh) is the unit of energy. 
One watt-hour is the energy consumed when 1 watt of power is used for 1 hour. 

Kilowatt-hour(kWh)

Kilowatt-hour is the commercial unit of energy 
The commercial unit of electric energy is kilowatt-hour (kWh), commonly known as ‘unit’. 

One kilowatt-hour is the energy consumed when 1 kilowatt of power is used for 1 hour. 

Relation between kilowatt-hour and joule 
Energy = Power x time
1 KWh = 1000 watt x 3600 second
             =  3.6 x \(10^6\) watt second
             =  3.6 x \(10^6\) joule (J)

NOW CHECK YOUR PROGRESS!!! 

1. Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes? 

2. Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V? 

3. Compare the power used in the 2 Ω resistor in each of the following circuits: (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors. 

4. Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A? 

5. An electric bulb is rated 220 V and 100 W. What will be the power consumed when it is operated at 110 V? 

6. An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h. 

7. An electric refrigerator rated 400 W operates 8 hour/day. What is the cost of the energy to operate it for 30 days at Rs 3.00 per kW h? 

8. An electric bulb is connected to a 220 V generator. The current is 0.50 A. What is the power of the bulb? 

Heating effect of electric current

HEATING EFFECT OF ELECTRIC CURRENT 

Electric current flowing through a conductor/wire also produces the heating effect across the length of the wire. You must have observed your electrical devices like television, fan, electric bulb etc get hot after operating them for few hours. This is simply the heating effect produced by electric current flowing in the device.

Work is done by the battery in supplying an electric current in a circuit. A part of the battery’s energy may be consumed into some useful work like in rotating the blades of an electric fan. Rest of the battery's energy may be expended in the form of heat to raise the temperature of gadget.
 
If the electric circuit is purely resistive, that is, we have a system of resistors only connected to a battery; the source energy continually gets dissipated entirely in the form of heat. This is known as the heating effect of electric current. This effect is utilised in devices such as electric heater, electric iron etc. 

Expression for heating effect of electric current 

Consider a purely resistive circuit, a resistor R connected to a voltage source V. Let current I flows through a resistor of resistance R. Let the potential difference across it be V. Let t be the time during which a charge Q flows across. The work done in moving the charge Q through a potential difference V is

\[W= VQ\]
Since \(Q=It\), therefore,
\[W=VIt\]
Using Ohm's law, \(V=IR\),
\[W=(IR)It\]
\[W=I^2Rt\]For purely resistive circuit, the work done by the battery gets dissipated in the resistor as heat.
\[H=I^2Rt\]

Joule’s Law of Heating 

According to Joule’s law of heating, heat produced in a resistor is 
(i) directly proportional to the square of current, 
(ii) directly proportional to resistance, and 
(iii) directly proportional to the time for which the current flows through the resistor. 
Thus,
\[H=I^2Rt\]

Undesirable effect of heating in electric circuit 

(1) Heating effect of electric current convert useful electrical energy into heat. 
(2) In electric circuits, the unavoidable heating increases the temperature of the gadget and alter their properties.

Practical Applications of Heating Effect of Electric Current 

(1) The electric laundry iron, electric toaster, electric oven, electric kettle and electric heater devices are based on Joule’s heating. 
(2) The electric heating is used to produce light, as in an electric bulb. 
(3) The functioning of fuse in electric circuit is based on joule’s heating.

Working of Electric iron, Electric toaster etc 

Alloys such as nichrome ( an alloy of nickel, chromium, manganese and iron), Constantan ( alloy of copper and nickel) and manganin (alloy of copper, manganese and nickel ) are used as an element of heating devices. Two properties which make these alloys suitable for heating element are: 
(a) High resistivity than metal. 
(b) Do not oxidise at higher temperature. 

When a large current is passed through these alloys then according to joule’s heating a large amount of heat is generated.

Working of Electric bulb 

The filament of electric bulb is made up of tungsten. The melting point of tungsten is very high ( 3380°C) When electric current is passed through tungsten filament it gets very hot and emits light. The filament is thermally isolated from the surrounding. The bulbs are usually filled with chemically inactive nitrogen and argon gases to prolong the life of filament. Most of the power consumed by the filament appears as heat, but a small part of it is in the form of light radiated. 


Two properties of tungsten which makes them suitable as filament of electric bulb 
(a) Very high melting point ( 3380°C) 
(b) Can be drawn into very thin wires 
(c) High resistivity than metals 

Electric Fuse 

Electric fuse protects circuits and appliances by stopping the flow of any unduly high electric current. It consists of a piece of wire made of a metal or an alloy of appropriate melting point, for example aluminium, copper, iron, lead etc. 

Working: If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases. This melts the fuse wire and breaks the circuit.

Capacity of fuse wire: The fuses used for domestic purposes are rated as 1 A, 2 A, 3 A, 5 A, 10 A, etc.
Connection of fuse wire in circuit: The fuse is placed in series with the device.

NOW CHECK YOUR PROGRESS!!! 

1. An electric heater of resistance 8 Ω draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater. 

2. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. Calculate the ratio of heat produced in series and parallel combinations. 

3. Two resistors each of resistance 6Ω are first connected in series and then parallel in a circuit across a battery of 10V. Calculate the ratio of heat produced in series and parallel combination. 

4. An electric iron of resistance 20 Ω takes a current of 5 A. Calculate the heat developed in 30 s.

5.Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V. 

6. 100 J of heat are produced each second in a 4 Ω resistance. Find the potential difference across the resistor. 

7. An electric iron consumes energy at a rate of 840 W when heating is at the maximum rate and 360 W when the heating is at the minimum. The voltage is 220 V. What are the current and the resistance in each case?