JEE Advanced PYQ Physics – Heating Effect of Current Questions with Solutions

Q 1 :

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances $R_{100}$ , $R_{60}$ and $R_{40}$ respectively, the relation between these resistances is [2010]

$\frac{1}{R_{100}} = \frac{1}{R_{40}} + \frac{1}{R_{60}}$
$R_{100} = R_{40} + R_{60}$
$R_{100} > R_{60} > R_{40}$
$\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$

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(4)

We know that power $P = \frac{V^{2}}{R}$

$∴$ For a constant V at a particular temperature, $P \propto \frac{1}{R}$

It is given that the power of the bulbs are in the order $100 W > 60 W > 40 W$

$∴$ $\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$

Q 2 :

Figure shows three resistor configurations $R_{1}$ , $R_{2}$ and $R_{3}$ connected to a 3 V battery. If the power dissipated by the configuration $R_{1}$ , $R_{2}$ and $R_{3}$ is $P_{1}$ , $P_{2}$ and $P_{3}$ , respectively, then [2008]

$P_{1} > P_{2} > P_{3}$
$P_{1} > P_{3} > P_{2}$
$P_{2} > P_{1} > P_{3}$
$P_{3} > P_{2} > P_{1}$

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4

(3)

We know power, $P = \frac{V^{2}}{R}$

And V is constant in all three cases. $∴$ $P \propto \frac{1}{R}$

Case (i)

This is a case of balanced Wheatstone bridge $R_{1} = 1 Ω$

Case (ii)

$\frac{1}{R_{2}} = \frac{1}{2} + \frac{1}{1} + \frac{1}{2}$ $\Rightarrow R_{2} = \frac{2}{4}$ $= \frac{1}{2} 52$

Case (iii)

Thus $R_{3} = 2 Ω$

$Since, R_{2} < R_{1} < R_{3}$ $∴$ $P_{2} > P_{1} > P_{3}$

Q 3 :

The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation. [2003]

III < II < IV < I
II < III < IV < I
I < IV < III < II
I < III < II < IV

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4

(1)

As we know, $P = I^{2} R$

Here $I$ is constant $∴$ $P \propto R$

Power dissipation, $P_{4} = I^{2} (\frac{3}{2} R) = 1.5 I^{2} R$

$∴$ $III < II < IV < I$

Q 4 :

A 100 W bulb $B_{1}$ and two 60 W bulbs $B_{2}$ and $B_{3}$ , are connected to a 250 V source, as shown in figure. Now $W_{1}$ , $W_{2}$ and $W_{3}$ are the output powers of the bulbs $B_{1}$ , $B_{2}$ and $B_{3}$ , respectively. Then [2002]

$W_{1} > W_{2} = W_{3}$
$W_{1} > W_{2} > W_{3}$
$W_{1} < W_{2} = W_{3}$
$W_{1} < W_{2} < W_{3}$

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(4)

As we know, $P = \frac{V^{2}}{R}$ $∴$ $R = \frac{V^{2}}{P}$

$∴$ $R_{1} = \frac{V^{2}}{100}, R_{2} = \frac{V^{2}}{60}, R_{3} = \frac{V^{2}}{60}$

$W_{1} = \frac{V_{1}^{2}}{R_{1}} = \frac{V^{2} R_{1}}{{(R_{1} + R_{2})}^{2}},$ $W_{2} = \frac{V_{2}^{2}}{R_{2}} = \frac{V^{2} R_{2}}{{(R_{1} + R_{2})}^{2}}$ and $W_{3} = \frac{V^{2}}{R_{3}}$

$W_{3} : W_{2} : W_{1} = \frac{{(250)}^{2}}{R_{3}} : \frac{{(250)}^{2} R_{2}}{{(R_{1} + R_{2})}^{2}} : \frac{{(250)}^{2} R_{1}}{{(R_{1} + R_{2})}^{2}}$

$= \frac{{(250)}^{2}}{V^{2}} \times 60 : \frac{{(250)}^{2}}{{(\frac{1}{100} + \frac{1}{60})}^{2}} \times \frac{V^{2}}{60} \times \frac{1}{V^{4}} : \frac{{(250)}^{2}}{{(\frac{1}{100} + \frac{1}{60})}^{2}} \times \frac{V^{2}}{100} \times \frac{1}{V^{4}}$

$= 60 : \frac{100 \times 100 \times 60 \times 60}{160 \times 160 \times 60} : \frac{100 \times 100 \times 60 \times 60}{160 \times 160 \times 100}$

$= 64 : 25 : 15$

$∴$ $W_{1} < W_{2} < W_{3}$

Q 5 :

When two identical batteries of internal resistance $1 Ω$ each are connected in series across a resistor $R$ , the rate of heat produced in $R$ is $J_{1}$ . When the same batteries are connected in parallel across $R$ , the rate is $J_{2}$ . If $J_{1} = 2.25 J_{2}$ then the value of $R$ in $Ω$ is [2010]

(4)

Cells connected in series

$J_{1} = I^{2} R = {(\frac{2 E}{2 r + R})}^{2} R$

Cells connected in parallel

$J_{2} = I^{2} R = {(\frac{E}{R + \frac{r}{2}})}^{2} R$

$∴$ $J_{1} = 2.25 J_{2} (Given)$

$\frac{{(2 E)}^{2}}{{(2 r + R)}^{2}} R = 2.25 \frac{E^{2}}{{(R + \frac{r}{2})}^{2}} R$

$\Rightarrow \frac{4}{{(2 r + R)}^{2}} = \frac{2.25}{{(R + \frac{r}{2})}^{2}}$

$\Rightarrow 4 {(R + 0.5)}^{2} = 2.25 {(2 + R)}^{2} [r = 1 Ω]$

$\Rightarrow 2 (R + 0.5) = 1.5 (2 + R)$

$∴$ $R = 4 Ω$

Q 6 :

In Circuit-1 and Circuit-2 shown in the figures, $R_{1} = 1 Ω$ , $R_{2} = 2 Ω$ and $R_{3} = 3 Ω$ .

$P_{1}$ and $P_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_{1}$ and $S_{2}$ are in open conditions, respectively.

$Q_{1}$ and $Q_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_{1}$ and $S_{2}$ are in closed conditions, respectively.

Which of the following statement(s) is(are) correct? [2022]

When a voltage source of 6 V is connected across A and B in both circuits, $P_{1} < P_{2}$ .
When a constant current source of 2 $A m p$ is connected across A and B in both circuits, $P_{1} > P_{2}$ .
When a voltage source of 6 V is connected across A and B in Circuit-1, $Q_{1} > P_{1}$ .
When a constant current source of $2 A m p$ is connected across A and B in both circuits, $Q_{2} < Q_{1}$ .

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Select one or more options

(3, 4)

When both switches are open

$R_{eq1} = \frac{16}{11} Ω, R_{eq2} = \frac{6}{11} Ω$

$So, R_{eq1} > R_{eq2}$

For voltage source, $P = \frac{V^{2}}{R_{eq}}$ $\Rightarrow P \propto \frac{1}{R_{eq}}$

$\Rightarrow P_{1} < P_{2} \Rightarrow (1) is correct.$

For constant current source, $P = i^{2} R_{eq}$

$\Rightarrow P \propto R_{eq}$

$\Rightarrow P_{1} > P_{2}$ $\Rightarrow (2) is correct.$

When switch is closed

$R'_{eq1} = \frac{5}{11} Ω, R'_{eq2} = \frac{1}{2} Ω$

$So, R'_{eq1} < R_{eq1}$

For voltage source

$P = \frac{V^{2}}{R}$ $\Rightarrow P \propto \frac{1}{R}$ $\Rightarrow Q_{1} > P_{1}$ $\Rightarrow (3) is correct.$

For current source

$P = i^{2} R$ $\Rightarrow P \propto R$ $\Rightarrow Q_{1} < Q_{2}$ $\Rightarrow (4) is incorrect.$

Q 7 :

Heater of an electric kettle is made of a wire of length L and diameter $d$ . It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter $2 d$ . The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K? [2014]

4 if wires are in parallel
2 if wires are in series
1 if wires are in series
0.5 if wires are in parallel

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4

Select one or more options

(2, 4)

Heat produced, $H = (\frac{V^{2}}{R}) t = \frac{V^{2}}{R} \times 4 \dots (i)$

$where R = ρ \frac{l}{A} = \frac{4 ρ l}{π d^{2}}$

When resistances are connected in series

$R_{total} = R_{1} + R_{2} = 2 (\frac{4 ρ l}{4 π d^{2}}) = 2 \times \frac{R}{4} = \frac{R}{2}$

$∴$ $H = \frac{V^{2}}{R / 2} \times t_{2} \dots (i i)$

From eq. (i) and (ii), $t_{2} = 2 min$

When resistances are connected in parallel

$R_{total} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} = \frac{R_{1}^{2}}{2 R_{1}} = \frac{R / 4}{2} = \frac{R}{8}$

$∴$ $H = \frac{V^{2}}{R / 8} \times t_{2} \dots (i i i)$

From eq. (i) and (iii), $t_{2} = 0.5 min$

Topic Question Set

Q 2 :

Figure shows three resistor configurations $R_{1}$ , $R_{2}$ and $R_{3}$ connected to a 3 V battery. If the power dissipated by the configuration $R_{1}$ , $R_{2}$ and $R_{3}$ is $P_{1}$ , $P_{2}$ and $P_{3}$ , respectively, then [2008]

Q 3 :

The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation. [2003]

Q 4 :

A 100 W bulb $B_{1}$ and two 60 W bulbs $B_{2}$ and $B_{3}$ , are connected to a 250 V source, as shown in figure. Now $W_{1}$ , $W_{2}$ and $W_{3}$ are the output powers of the bulbs $B_{1}$ , $B_{2}$ and $B_{3}$ , respectively. Then [2002]

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Topic Question Set

Q 1 : Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R100, R60 and R40 respectively, the relation between these resistances is [2010]

Q 2 : Figure shows three resistor configurations R1, R2 and R3 connected to a 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then [2008]

Q 3 : The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation. [2003]

Q 4 : A 100 W bulb B1 and two 60 W bulbs B2 and B3, are connected to a 250 V source, as shown in figure. Now W1, W2 and W3 are the output powers of the bulbs B1, B2 and B3, respectively. Then [2002]

Q 5 : When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1=2.25 J2 then the value of R in Ω is [2010]

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Q 2 :

Figure shows three resistor configurations $R_{1}$ , $R_{2}$ and $R_{3}$ connected to a 3 V battery. If the power dissipated by the configuration $R_{1}$ , $R_{2}$ and $R_{3}$ is $P_{1}$ , $P_{2}$ and $P_{3}$ , respectively, then [2008]

Q 3 :

The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation. [2003]

Q 4 :

A 100 W bulb $B_{1}$ and two 60 W bulbs $B_{2}$ and $B_{3}$ , are connected to a 250 V source, as shown in figure. Now $W_{1}$ , $W_{2}$ and $W_{3}$ are the output powers of the bulbs $B_{1}$ , $B_{2}$ and $B_{3}$ , respectively. Then [2002]