Electricity — Class 10 Science
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Chapter summary
Key ideas & terms
- Electric current
- Rate of flow of electric charge, measured in amperes.
- Ohm’s law
— current is proportional to potential difference at constant temperature. - Resistance
- Opposition to current flow, measured in ohms.
- Electric power
- Rate of consuming electrical energy,
.
Extra questions & answers
Why are series circuits not used for domestic wiring?
In series, all appliances share one current and switch off together if one fails; parallel wiring gives each appliance full voltage and independent control.
Why is tungsten used for the filament of an electric bulb?
It has a very high melting point and high resistivity, so it glows white-hot without melting.
Define electric current and state its SI unit.
Electric current is the rate of flow of electric charge through a conductor; its SI unit is the ampere (A).
What is potential difference, and how is it measured?
The work done to move a unit charge between two points; it is measured in volts (V) using a voltmeter connected in parallel.
State Ohm’s law.
At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends:
On what factors does the resistance of a conductor depend?
On its length (directly), its area of cross-section (inversely), the material (resistivity) and the temperature.
How does the net resistance change in series and in parallel?
In series the resistances add up
Why is parallel arrangement used in domestic wiring?
Because each appliance then gets the full supply voltage, can be switched on or off independently, and the failure of one does not stop the others (refer to the circuit diagram in your NCERT textbook).
State the heating effect of current and one application.
When current flows through a resistor, heat is produced, given by
Define electric power and the commercial unit of electrical energy.
Electric power is the rate of consuming electrical energy,
QUESTIONS
1. What does an electric circuit mean?
An electric circuit is a continuous, closed conducting path through which electric current can flow.
2. Define the unit of current.
The SI unit of electric current is the ampere. A current of 1
,
mathrmA flows when 1
,
mathrmC of charge passes through a cross-section of a conductor in 1
,
mathrms:
3. Calculate the number of electrons constituting one coulomb of charge.
The magnitude of the charge on one electron is 1.6
times10
−19
,
mathrmC. Therefore,
times10
18
electrons constitute one coulomb of charge.
QUESTIONS
1. Name a device that helps to maintain a potential difference across a conductor.
An electric cell or a battery maintains a potential difference across a conductor.
2. What is meant by saying that the potential difference between two points is 1
,
mathrmV?
The potential difference between two points is 1
,
mathrmV when 1
,
mathrmJ of work is required to move 1
,
mathrmC of charge from one point to the other:
3. How much energy is given to each coulomb of charge passing through a 6
,
mathrmV battery?
Using W=VQ, for Q=1
,
mathrmC and V=6
,
mathrmV,
,
mathrmJ of energy.
QUESTIONS
1. On what factors does the resistance of a conductor depend?
The resistance of a conductor depends on its length, its area of cross-section, the nature of its material and its temperature. For a uniform conductor at a fixed temperature,
2. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?
Current will flow more easily through the thick wire. A thick wire has a larger cross-sectional area, so its resistance is lower because R
propto
frac1A. The same source therefore produces a larger current through it.
3. 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?
According to Ohm’s law, I=
fracVR. If the resistance remains constant and the potential difference becomes half, the current also becomes half of its former value.
4. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?
Alloys are used because they generally have higher resistivity than pure metals, can withstand high temperatures and do not oxidise readily when heated. They therefore produce sufficient heat and last longer.
5. Use the data in Table 11.2 to answer the following – (a) Which among iron and mercury is a better conductor?
Iron is the better conductor because its resistivity, 10.0
times10
−8
,
Omega
,
mathrmm, is lower than that of mercury, 94.0
times10
−8
,
Omega
,
mathrmm.
(b) Which material is the best conductor?
Silver is the best conductor among the materials listed because it has the lowest resistivity, 1.60
times10
−8
,
Omega
,
mathrmm.
QUESTIONS
1. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2
,
mathrmV each, a 5
,
Omega resistor, an 8
,
Omega resistor, and a 12
,
Omega resistor, and a plug key, all connected in series.
The circuit should be drawn as one closed series loop containing a battery of three 2
,
mathrmV cells, a plug key and the 5
,
Omega, 8
,
Omega and 12
,
Omega resistors connected one after another. The total battery voltage is 6
,
mathrmV.
2. Redraw the circuit of Question 1, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12
,
Omega resistor. What would be the readings in the ammeter and the voltmeter?
The ammeter should be connected in series with the resistors, while the voltmeter should be connected in parallel across the 12
,
Omega resistor. The total resistance is
QUESTIONS
1. Judge the equivalent resistance when the following are connected in parallel – (a) 1
,
Omega and 10
6
,
Omega, (b) 1
,
Omega and 10
3
,
Omega, and 10
6
,
Omega.
For part (a),
,
Omega. For part (b),
,
Omega.
2. An electric lamp of 100
,
Omega, a toaster of resistance 50
,
Omega, and a water filter of resistance 500
,
Omega are connected in parallel to a 220
,
mathrmV source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?
The currents through the three appliances are
,
mathrmA. Its resistance is
3. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
In a parallel connection, every device receives the full supply voltage and can draw the current required for its proper operation. Each device can also be switched on or off independently, and the failure of one device does not stop the others from working.
4. How can three resistors of resistances 2
,
Omega, 3
,
Omega, and 6
,
Omega be connected to give a total resistance of (a) 4
,
Omega, (b) 1
,
Omega?
For part (a), connect the 3
,
Omega and 6
,
Omega resistors in parallel. Their equivalent resistance is
,
Omega resistor to obtain
,
Omega.
5. What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistance 4
,
Omega, 8
,
Omega, 12
,
Omega, 24
,
Omega?
The highest resistance is obtained by connecting all four coils in series:
QUESTIONS
1. Why does the cord of an electric heater not glow while the heating element does?
The connecting cord has very low resistance and therefore produces little heat. The heating element has much higher resistance, so it produces a large amount of heat according to H=I
2
Rt, becomes red hot and glows.
2. Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50
,
mathrmV.
The electrical energy converted into heat is
3. An electric iron of resistance 20
,
Omega takes a current of 5
,
mathrmA. Calculate the heat developed in 30
,
mathrms.
Using Joule’s law of heating,
times10
4
,
mathrmJ.
QUESTIONS
1. What determines the rate at which energy is delivered by a current?
Electric power determines the rate at which electrical energy is delivered or consumed. It is given by
2. An electric motor takes 5
,
mathrmA from a 220
,
mathrmV line. Determine the power of the motor and the energy consumed in 2
,
mathrmh.
The power of the motor is
,
mathrmh is
EXERCISES
1. 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 the ratio R/R′ is – (a) 1/25 (b) 1/5 (c) 5 (d) 25
Each part has resistance R/5. Five equal resistances of R/5 connected in parallel have equivalent resistance
2. Which of the following terms does not represent electrical power in a circuit? (a) I
2
R (b) IR
2
(c) VI (d) V
2
/R
Electrical power can be written as P=VI, P=I
2
R or P=
fracV
2
R. Therefore, IR
2
does not represent electrical power. The correct option is (b).
3. An electric bulb is rated 220
,
mathrmV and 100
,
mathrmW. When it is operated on 110
,
mathrmV, the power consumed will be – (a) 100
,
mathrmW (b) 75
,
mathrmW (c) 50
,
mathrmW (d) 25
,
mathrmW
The resistance of the bulb is
,
mathrmV,
,
mathrmW.
4. 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. The ratio of heat produced in series and parallel combinations would be – (a) 1:2 (b) 2:1 (c) 1:4 (d) 4:1
Let the resistance of each wire be R. In series, the equivalent resistance is 2R; in parallel, it is R/2. For the same voltage and time, H=
fracV
2
tR. Hence,
5. How is a voltmeter connected in the circuit to measure the potential difference between two points?
A voltmeter is connected in parallel across the two points between which the potential difference is to be measured.
6. A copper wire has diameter 0.5
,
mathrmmm and resistivity of 1.6
times10
−8
,
Omega
,
mathrmm. What will be the length of this wire to make its resistance 10
,
Omega? How much does the resistance change if the diameter is doubled?
The radius is
rhol/A,
,
Omega.
7. 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
(
mathrmamperes)
quad0.5
quad1.0
quad2.0
quad3.0
quad4.0 V
(
mathrmvolts)
quad1.6
quad3.4
quad6.7
quad10.2
quad13.2 Plot a graph between V and I and calculate the resistance of that resistor.
Plot I on the horizontal axis and V on the vertical axis. The plotted points lie approximately on a straight line through the origin. The resistance equals the slope of the V−I graph:
,
Omega.
8. When a 12
,
mathrmV battery is connected across an unknown resistor, there is a current of 2.5
,
mathrmmA in the circuit. Find the value of the resistance of the resistor.
Convert the current to amperes:
9. A battery of 9
,
mathrmV is connected in series with resistors of 0.2
,
Omega, 0.3
,
Omega, 0.4
,
Omega, 0.5
,
Omega and 12
,
Omega, respectively. How much current would flow through the 12
,
Omega resistor?
The total series resistance is
,
mathrmA flows through the 12
,
Omega resistor.
10. How many 176
,
Omega resistors (in parallel) are required to carry 5
,
mathrmA on a 220
,
mathrmV line?
The current through one resistor is
11. Show how you would connect three resistors, each of resistance 6
,
Omega, so that the combination has a resistance of (i) 9
,
Omega, (ii) 4
,
Omega.
For (i), connect two 6
,
Omega resistors in parallel, giving
,
Omega resistor to obtain 9
,
Omega. For (ii), connect two 6
,
Omega resistors in series to obtain 12
,
Omega, and connect this series combination in parallel with the third 6
,
Omega resistor:
12. Several electric bulbs designed to be used on a 220
,
mathrmV electric supply line, are rated 10
,
mathrmW. How many lamps can be connected in parallel with each other across the two wires of 220
,
mathrmV line if the maximum allowable current is 5
,
mathrmA?
The current drawn by one lamp is
13. A hot plate of an electric oven connected to a 220
,
mathrmV line has two resistance coils A and B, each of 24
,
Omega resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
When one coil is used separately,
14. Compare the power used in the 2
,
Omega resistor in each of the following circuits: (i) a 6
,
mathrmV battery in series with 1
,
Omega and 2
,
Omega resistors, and (ii) a 4
,
mathrmV battery in parallel with 12
,
Omega and 2
,
Omega resistors.
In circuit (i), the total resistance is 3
,
Omega, so
,
Omega resistor is
,
mathrmV is across the 2
,
Omega resistor:
,
mathrmW, in both circuits.
15. Two lamps, one rated 100
,
mathrmW at 220
,
mathrmV, and the other 60
,
mathrmW at 220
,
mathrmV, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220
,
mathrmV?
The total power is
16. Which uses more energy, a 250
,
mathrmW TV set in 1
,
mathrmhr, or a 1200
,
mathrmW toaster in 10 minutes?
The TV uses
,
mathrmh, and uses
17. An electric heater of resistance 44
,
Omega draws 5
,
mathrmA from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.
The rate at which heat is developed is the electric power:
,
mathrmJ,s
−1
, or 1.1
,
mathrmkW.
18. Explain the following. (a) Why is the tungsten used almost exclusively for filament of electric lamps?
Tungsten has a very high melting point and high resistivity. It can therefore become white hot and emit light without melting quickly.
(b) Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?
Alloys generally have higher resistivity than their constituent pure metals, have high melting points and do not oxidise readily at high temperatures. They therefore produce more heat and remain durable.
(c) Why is the series arrangement not used for domestic circuits?
A series arrangement would divide the supply voltage among appliances, and the same current would have to pass through every appliance even though they require different currents. Moreover, switching off or failure of one appliance would break the entire circuit. Domestic appliances are therefore connected in parallel.
(d) How does the resistance of a wire vary with its area of cross-section?
For a wire of fixed material, length and temperature, resistance is inversely proportional to its cross-sectional area:
(e) Why are copper and aluminium wires usually employed for electricity transmission?
Copper and aluminium have very low resistivity, so they conduct electricity well and lose comparatively little electrical energy as heat. They are also sufficiently ductile to be made into long wires.