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#### Question 1:

A cell, a resistor, a key and ammeter are arranged as shown in the circuit diagrams of Figure12.1. The current recorded in the ammeter will be

(a) maximum in (i)
(b) maximum in (ii)
(c) maximum in (iii)
(d) the same in all the cases

Since the resistance is same in all the three circuit diagrams so the current will be same in all the three cases.
Hence, the correct answer is option D.

#### Question 2:

In the following circuits (Figure 12.2), heat produced in the resistor or combination of resistors connected to a 12 V battery will be

(a) same in all the cases
(b) minimum in case (i)
(c) maximum in case (ii)
(d) maximum in case (iii)

Heat produced in time (t) is given by
Heat (H) = $\frac{{V}^{2}}{R}×t$
where, V = potential difference
R = Net resistance of the circuit
t = time

Since, ${R}_{3net}$ is minimum so heat produced will be maximum in case (iii)
Hence, the corrrect answer is option D.

#### Question 3:

Electrical resistivity of a given metallic wire depends upon
(a) its length
(b) its thickness
(c) its shape
(d) nature of the material

Electrical resistivity of a given metallic wire depends upon the nature of the material.
Hence, the correct answer is option D

#### Question 4:

A current of 1 A is drawn by a filament of an electric bulb. Number of electrons passing through a cross section of the filament in 16 seconds would be roughly
(a) 1020
(b) 1016
(c) 1018
(d) 1023

Current, i = 1 A
Time, t = 16 s
We know
$i=\frac{q}{t}\phantom{\rule{0ex}{0ex}}q=i×t$

Now,
$q=n×e$
where, n is number of electrons lost or gained
e = charge on 1 electron ()

Hence, the correct answer is option A

#### Question 5:

Identify the circuit (Figure 12.3) in which the electrical components have been properly connected.

(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

All the electrical components have been correctly connected in case (ii). This is because ammeter is connected in series and voltmeter is connected parallel to the resistor. Moreover, terminal of both the devices connected to positive terminal of the cell must be positive.
Hence, the correct answer is option B.

#### Question 6:

What is the maximum resistance which can be made using five resistors each of 1/5 Ω?
(a) 1/5 Ω
(b) 10 Ω
(c) 5 Ω
(d) 1 Ω

Resistance will be maximum when all the five resistors are connected in series.

Hence, the correct answer is option D.

#### Question 7:

What is the minimum resistance which can be made using five resistors each of 1/5 Ω?
(a) 1/5 Ω
(b) 1/25 Ω
(c) 1/10 Ω
(d) 25 Ω

Resistance will be minimum when all the five resistors are in parallel connection. Since all the five resistors are identical so the formula will be

Hence, the correct answer is option B.

#### Question 8:

The proper representation of series combination of cells (Figure 12.4) obtaining maximum potential is

(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

The positive terminal of a cell should be connected to the negative terminal of the adjacent cell. Case (i) represents the correct combination of cells.
Hence, the correct answer is option A.

#### Question 9:

Which of the following represents voltage?

(a)

(b) Work done × Charge

(c)

(d) Work done × Charge × Time

Potential difference (V) is defined as the ratio of work done (W) and charge (Q).
$V=\frac{W}{Q}$

Charge is defined as
$Q=i×t$
where i = current
t = time

So,
$V=\frac{W}{i×t}$

Hence, the correct answer is option A.

#### Question 10:

A cylindrical conductor of length l and uniform area of cross section A has resistance R. Another conductor of length 2l and resistance R of the same material has area of cross section
(a) A/2
(b) 3A/2
(c) 2A
(d) 3A

Let the resistivity of the material be $\rho$
Resistance (R) of the first cylindrical conductor$=\frac{\rho l}{A}$
where, l = length of conductor
A = area of cross section

Now, another cylindrical conductor has double length but same resistance.
Let its area of cross section be A'
Its resistance (R') will be = $\frac{\rho ×2l}{A\text{'}}$
Since resistance is same
R = R'
$\frac{\rho ×l}{A}=\frac{\rho ×2l}{A\text{'}}$

Solving it, we get A' = 2A

Hence, the correct answer is option C.

#### Question 11:

A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistances R1, R2 and R3 respectively (Figure.12.5). Which of the following is true?

(a) R1 = R2 = R3
(b) R1 > R2 > R3
(c) R3 > R2 > R1
(d) R2 > R3 > R1

Since the current (I) is plotted on y-axis and potential difference (V) is plotted on x-axis, so the slope of the graph is $\frac{1}{R}$. It means higher the slope, the lesser is the resistance. So, ${R}_{1}$ will be minimum and ${R}_{3}$ will be maximum.
Hence, the correct answer is option C.

#### Question 12:

If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be
(a) 100 %
(b) 200 %
(c) 300 %
(d) 400 %

If the current is increased by 100% then the current will become twice i.e 2I. The power dissipated through a resistor is given by
$P={I}^{2}R$
If the current is made twice then power dissipated will become four times.
i.e. P' = 4 P
The percentage increase in power is given as,

Hence, the correct answer is option C.

#### Question 13:

The resistivity does not change if
(a) the material is changed
(b) the temperature is changed
(c) the shape of the resistor is changed
(d) both material and temperature are changed

Resistivity of a material depends only on the temperature and the nature of material. Shape of the resistor has no effect on the resistivity.
Hence, the correct answer is option C.

#### Question 14:

In an electrical circuit three incandescent bulbs A, B and C of rating 40 W, 60 W and 100 W respectively are connected in parallel to an electric source. Which of the following is likely to happen regarding their brightness?
(a) Brightness of all the bulbs will be the same
(b) Brightness of bulb A will be the maximum
(c) Brightness of bulb B will be more than that of A
(d) Brightness of bulb C will be less than that of B

Since all the three bulbs are connected in parallel so potential difference (V) across all the bulbs is same. Power dissipated is given by
$P=\frac{{V}^{2}}{R}$

Lower the resistance, higher the power dissipation. Hence higher the brightness.
Out of all the three bulbs, 100 W bulb will have minimum resistance because rated voltage of all the bulbs will be same  and its power dissipation is maximum.
Thus, 100 W will have maximum brightness and 40 W bulb will have minimum brightness.
Hence, the correct answer is option C.

#### Question 15:

In an electrical circuit two resistors of 2 $\mathrm{\Omega }$ and 4 $\mathrm{\Omega }$ respectively are connected in series to a 6 V battery. The heat dissipated by the 4 $\mathrm{\Omega }$ resistor in 5 s will be
(a) 5 J
(b) 10 J
(c) 20 J
(d) 30 J

Since and  are connected in series so their net resistance is
${R}_{net}={R}_{1}+{R}_{2}$

Current (I) in the circuit is given by

Heat dissipated through  resistor is given by

Hence, the correct answer is option C.

#### Question 16:

An electric kettle consumes 1 kW of electric power when operated at 220 V. A fuse wire of what rating must be used for it?
(a) 1 A
(b) 2 A
(c) 4 A
(d) 5 A

Power (P) = 1 kW = 1000 W
Potential difference (V) = 220 V
We know,
P = VI

From all the given options, 5 A fuse wire is correct
Hence, the correct answer is option D.

#### Question 17:

Two resistors of resistance 2 Ω and 4 Ω when connected to a battery will have
(a) same current flowing through them when connected in parallel
(b) same current flowing through them when connected in series
(c) same potential difference across them when connected in series
(d) different potential difference across them when connected in parallel

When two resistors are connected in series with a battery then current passing through them is same.
Hence, the correct answer is option B.

#### Question 18:

Unit of electric power may also be expressed as
(a) volt ampere
(b) kilowatt hour
(c) watt second
(d) joule second

Power is defined as
P = VI
where, V = Potential difference (Volt)
I = Current (Ampere)

So, unit of electric power may also be expressed as volt ampere.
Hence, the correct answer is option A.

#### Question 19:

A child has drawn the electric circuit to study Ohm’s law as shown in Figure 12.6. His teacher told that the circuit diagram needs correction. Study the circuit diagram and redraw it after making all corrections.

The correct circuit diagram is shown as below

#### Question 20:

Three 2 Ω resistors, A, B and C, are connected as shown in Figure 12.7. Each of them dissipates energy and can withstand a maximum power of 18 W without melting. Find the maximum current that can flow through the three resistors?

where,
P = Potential difference
I = Current
R = Resistance

For resistor A,

This is the maximum current that can flow through the resistor A.

The maximum current flowing through the resistors B and C,

#### Question 21:

Should the resistance of an ammeter be low or high? Give reason.

Resistance of an ammeter should ideally be zero so that it does not affect the flow of current in the circuit. Hence, resistance of an ammeter should be very low as zero resistance is not possible in real life.

#### Question 22:

Draw a circuit diagram of an electric circuit containing a cell, a key, an ammeter, a resistor of 2Ω in series with a combination of two resistors (4Ω each) in parallel and a voltmeter across the parallel combination. Will the potential difference across the 2Ω resistor be the same as that across the parallel combination of 4Ω resistors? Give reason.

Net resistance of two  resistors connected in parallel is . Since we have two resistors of same resistance in series so the potential drop across each one of them will be same.

#### Question 23:

How does use of a fuse wire protect electrical appliances?

Fuse wire has low melting point and high resistance. So, whenever there is surge in the electric current, the fuse wire melts and breaks the circuit. This prevents any damage to the electrical appliances. Thus, a fuse wire protects the electrical appliances.

#### Question 24:

What is electrical resistivity? In a series electrical circuit comprising a resistor made up of a metallic wire, the ammeter reads 5 A. The reading of the ammeter decreases to half when the length of the wire is doubled. Why?

Electrical resistivity is the inherent property of the resistor because of which it opposes the flow of electric current. It depends only on the nature and temperature of the resistor.
Resistance varies as directly proportional with the length. When the length is doubled then resistance also become double. Current is inversely proportional to resistance according to Ohm's law. If the resistance becomes double then current will become half i.e 5 A to 2.5 A.
This is why the reading of the ammeter decreases to half.

#### Question 25:

What is the commercial unit of electrical energy? Represent it in terms of joules.

The commercial unit of electrical energy is Kilowatt hour (kWh)

#### Question 26:

A current of 1 ampere flows in a series circuit containing an electric lamp and a conductor of 5 Ω when connected to a 10 V battery. Calculate the resistance of the electric lamp.

Now if a resistance of 10 Ω is connected in parallel with this series combination, what change (if any) in current flowing through 5 Ω conductor and potential difference across the lamp will take place? Give reason.

Let the resistance of the electric lamp be ${R}_{lamp}$.
Current (I) = 1 A
Resistance of conductor (${R}_{conductor}$) =
Potential difference of battery (V) = 10 V

Since the lamp and the conductor is connected in series, thus same current 1 A will pass through both of them.

Using Ohm's law,

We know in series connection:

Potential difference across lamp,

When  resistor is connected parallel to the series combination of lamp and conductor  then the equivalent resistance,

Using Ohm's law

Current will distribute equally in two parallel parts.
Thus,   current will pass through both the lamp and the resistor of  (because they are connected in series).
Potential difference across the lamp ,

Hence, there will be no change in current through the conductor of resistance , and potential difference across the lamp.

#### Question 27:

Why is parallel arrangement used in domestic wiring?

Parallel arrangement is used in domestic wiring because of the following reasons
1. Net resistance of the electric circuit decreases in parallel connection as compared to series connection due to which heat loss is reduced.
2. Potential difference across each electrical device remains same i.e 220 V due to which all the electrical devices work upto their maximum potential.
3. Each electrical device can be operated independently.
4. If one electrical device stops working still other electrical devices continue to work properly.

#### Question 28:

B1, B2 and B3 are three identical bulbs connected as shown in Figure 12.8. When all the three bulbs glow, a current of 3A is recorded by the ammeter A.

(i) What happens to the glow of the other two bulbs when the bulb B1 gets fused?
(ii) What happens to the reading of A1, A2, A3 and A when the bulb B2 gets fused?
(iii) How much power is dissipated in the circuit when all the three bulbs glow together?

Since all the three bulbs are identical so current through each bulb will remain same i.e 1 A

(i) Even when bulb ${B}_{1}$ gets fused, other two bulbs will continue to glow with same brightness because all the three bulbs are connected in parallel so potential difference across each bulb remains same.

(ii) When bulb ${B}_{2}$ gets fused then the reading ${A}_{2}$ will become zero. The reading of and ${A}_{3}$ will remain same as 1 A because potential difference across them remains same. However, the reading of A will decrease and will become 2 A.

(iii). Power dissipated by bulb ${B}_{1}$ will be

Similarly,

Hence total power dissipated by the circuit will be

#### Question 29:

Three incandescent bulbs of 100 W each are connected in series in an electric circuit. In another circuit another set of three bulbs of the same wattage are connected in parallel to the same source.
(a) Will the bulb in the two circuits glow with the same brightness? Justify your answer.
(b) Now let one bulb in both the circuits get fused. Will the rest of the bulbs continue to glow in each circuit? Give reason.

(a) In series combination, potential difference get divided whereas in parallel potential difference across each bulb remains full. Hence in series bulbs glow with less brightness as compared to the bulbs in parallel connection.

(b) Now if one bulb gets fused in series connection then all the other bulbs will stop glowing whereas in parallel connection other bulbs will continue to glow. This is because in series combination even a single faulty component break the circuit whereas this does not happen in parallel circuit.

#### Question 30:

State Ohm’s law? How can it be verified experimentally? Does it hold good under all conditions? Comment.

Ohm's Law states that at constant temperature, potential difference across a conductor is directly proportional to the current passing through it.
Mathematically

where,
V = potential difference
I = current
R = Constant of proportionality and it is called Resistance

Experimental verification of Ohm's law:
Material needed: a nichrome wire,  an ammeter, a voltmeter, three cells, key etc.,
Procedure:
1. Create a circuit as shown in the diagram, consisting of a nichrome wire XY of length, say 0.4 m, an ammeter, a voltmeter and three cells of 1 V each. Place all the equipment properly.

2. First use only one cell as the source in the circuit. Note the reading in the ammeter I, for the current and reading of the voltmeter V for the potential difference across the nichrome wire XY in the circuit. Mark the corresponding readings in the Table given.
3. Now connect two cells in the circuit and note the respective readings of the ammeter and voltmeter for the values of current through the nichrome wire and potential difference across the nichrome wire.
4. Calculate the ratio of potential difference V to current I for each step.
5. Then plot the graph between potential difference and the current.

 S No. Number of cells used Current (I) Potential difference (R) Ratio(V/I) 1 1 2 2 3 3

The graph between potential difference and the current is observed to be a straight line passing through origin. The slope of V-I graph indicates the resistance of the circuit. This verifies Ohm's law.

Ohm's law does not hold good under all conditions. It is obeyed by metallic conductors only when physical conditions like temperature etc. are kept unchanged and ideal. It is not obeyed by semiconductors, junction diode, thermistor etc. These are called non-ohmic conductors.

#### Question 31:

What is electrical resistivity of a material? What is its unit? Describe an experiment to study the factors on which the resistance of conducting wire depends.

Electrical resistivity is the inherent property of a conductor due to which it opposes the flow of current in the wire. It does not depend on the length and area of cross section of wire. It depends only on the temperature and nature of the material of the wire.
Its SI unit is $\mathrm{\Omega m}$ (Ohm metre).
Experiment to study the factors on which the resistance of conducting wire depends:

Materials needed:  nichrome wires and copper wires of specified dimensions as described below, an ammeter,  a cell, a key etc.,
1. Set up an electric circuit consisting of a cell, an ammeter, a nichrome wire of length l [say, marked (1)] and a plug key, as shown in the diagram.

2. Now, plug the key. Note the current in the ammeter.
3. Replace the nichrome wire with another nichrome wire of the same thickness but twice the length, that is 2l [marked (2)]. Note the ammeter reading.
4. Now replace the wire with a thicker nichrome wire of larger cross-sectional area and of the same length l [marked (3)]. Again note down the current through the circuit.
5. Now instead of taking a nichrome wire, connect a copper wire [marked (4) ] in the circuit. Let the wire be of the same length and same area of cross-section as that of the first nichrome wire [marked (1)]. Note the value of the current. Notice the difference in the current in all cases.
6. Tabulate all the readings and calculate the resistance from the ratio of potential difference V and current I

It is observed that the resistance of the wire increases with the increase in length of the nichrome wire and decreases with the increase in the area of cross-section.
If we replace the nichrome wire with copper wire of the same length and area of cross-section even then resistance will be different.
These observations show that the resistance of a wire depends on the length, area of cross-section and nature of the material.

#### Question 32:

How will you infer with the help of an experiment that the same current flows through every part of the circuit containing three resistances in series connected to a battery?

Take three resistances
1. Connect them in series combination using battery, ammeter and key as shown in the diagram.

2. First of all, connect the ammeter between battery and ${R}_{1}$ and note down the reading.
3. After that, connect the ammeter between ${R}_{1}$ and ${R}_{2}$ and note down the reading.
4. After that, connect the ammeter between ${R}_{3}$ and battery.
5. Note down the reading of the ammeter in each steps.

It is observed that ammeter shows the same reading in all the three situations. This shows that same current flows through all the three resistors.

#### Question 33:

How will you conclude that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery?

1. Take three resistors and ${R}_{3}$ and connect them in parallel arrangement as shown in the diagram.

2. Connect voltmeter in parallel to measure the potential difference across the combination.
3. Now measure the potential difference across the resistor ${R}_{1}$ by connecting the voltmeter across it.

4. Again, measure the potential difference across the resistor ${R}_{2}$ by connecting the voltmeter across it.
5.  Again, measure the potential difference across the resistor ${R}_{3}$ by connecting the voltmeter across it.
6. Tabulate all the readings.

It is observed that potential difference reading will be same in all the three cases. This shows that the same potential difference exists across three resistors connected in parallel arrangement to a battery.

#### Question 34:

What is Joule’s heating effect? How can it be demonstrated experimentally? List its four applications in daily life.

Joule's law of heating states that heat produced in the resistor is
1. directly proportional to the square of the current.
2. directly proportional to the resistance.
3. directly proportional to the current.

Mathematically,
$H={i}^{2}Rt$
where,
H = Heat produced
I = Current
R = Resistance
t = time

Experimental demonstration
1. Take a water heating immersion rod, water, bucket, thermometer, regulator.
2. Immerse the water heating immersion rod in the water and measure the time taken to heat the water upto a certain temperature.
3. Now increase the current to double with the help of regulator and now measure the time taken to heat the water upto the same temperature.
Then, we will observe that time taken in second case will be one fourth the time taken in earlier case. Hence, it verifies the Joule's law of heating.

Electric fuse, toaster, oven, kettle,  are the four applications of Joule's law of heating in daily life.

#### Question 35:

Find out the following in the electric circuit given in Figure 12.9
(a) Effective resistance of two 8 Ω resistors in the combination
(b) Current flowing through 4 Ω resistor
(c) Potential difference across 4 Ω resistance
(d) Power dissipated in 4 Ω resistor
(e) Difference in ammeter readings, if any.

(a) Both  resistors are connected in parallel so the effective resistance of the two will be

(b) Net resistance of the circuit will be

So, current in resistor using Ohm's law is

(c) Potential difference across  resistor is

(d) Power dissipated through  is

(e) Both ammeters ${A}_{1}$ and ${A}_{2}$ will record same readings because they are connected in series. Hence difference in their readings will be zero.

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