Heating Effect of Current and Electrical Measuring Instruments

Q 11 :

Ratio of thermal energy released in two resistor $R$ and $3 R$ connected in parallel in an electric circuit is [2023]

3 : 1
1 : 1
1 : 3
1 : 27

1

2

3

4

(1)

$H = \frac{V^{2}}{R} \times t$

$\frac{H_{1}}{H_{2}} = \frac{\frac{V^{2} t}{R}}{\frac{V^{2} t}{3 R}} = 3 : 1$

Q 12 :

The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will be [2023]

$H$
$16 H$
$\frac{H}{4}$
$4 H$

1

2

3

4

(2)

$H \propto i^{2} for t = constant$

$\frac{H}{H'} = {(\frac{4}{16})}^{2}$

$H' = 16 H$

Q 13 :

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be: [2023]

4 : 1
2 : 1
1 : 2
1 : 4

1

2

3

4

(1)

$Parallel combination;$

$H_{P} = (\frac{V^{2}}{(\frac{R}{2})}) t = \frac{2 V^{2} t}{R}$

$Series combination;$

$H_{S} = (\frac{V^{2}}{2 R}) t$

$∴$ $\frac{H_{P}}{H_{S}} = 4$

Q 14 :

Different combination of 3 resistors of equal resistance R are shown in the figures.

The increasing order for power dissipation is: [2023]

$P_{A} < P_{B} < P_{C} < P_{D}$
$P_{C} < P_{D} < P_{A} < P_{B}$
$P_{B} < P_{C} < P_{D} < P_{A}$
$P_{C} < P_{B} < P_{A} < P_{D}$

1

2

3

4

(4)

$P = i^{2} R$

$R_{1} = \frac{3 R}{2}, R_{2} = \frac{2 R}{3}, R_{3} = \frac{R}{3}, R_{4} = 3 R$

$Since i is same, hence P \propto R, so option (4) is correct.$

Q 15 :

A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J ${kg}^{- 1}$ $K^{- 1}$ . The efficiency of heater is 70%. Time required to heat 2 kg of water from 10°C to 60°C is __________ s.

(Assume that the specific heat capacity of water remains constant over the temperature range of the water.) [2023]

0%

(300)

$η \times P \times Δ t = M \times s \times Δ T$

$\Rightarrow Δ t = \frac{2 \times 4200 \times (60 - 10)}{0.7 \times 2000} s = 300 s$

Q 16 :

A potential $V_{0}$ is applied across a uniform wire of resistance $R$ . The power dissipation is $P_{1}$ . The wire is then cut into two equal halves and a potential of $V_{0}$ is applied across the length of each half. The total power dissipation across two wires is $P_{2}$ . The ratio $P_{2} : P_{1}$ is $\sqrt{x} : 1$ . The value of $x$ is _______. [2023]

0%

(16)

$P = V I = I^{2} R = \frac{V^{2}}{R}$

$Now R = \frac{ρ ℓ}{A}$

$If the wire is cut into two equal half, R = \frac{R}{2}$

$Initial P_{1} = \frac{V_{0}^{2}}{R}$

$After P_{2} = \frac{V_{0}^{2}}{R'} \times 2 \Rightarrow \frac{V_{0}^{2}}{R} \times 4$

$\frac{P_{2}}{P_{1}} = 4 = \frac{\sqrt{x}}{1} \Rightarrow x = 16$

Q 17 :

The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1 $Ω$ is connected across these points is __________ J. [2026]

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1080

Topic Question Set

Q 11 :

Ratio of thermal energy released in two resistor $R$ and $3 R$ connected in parallel in an electric circuit is [2023]

Q 12 :

The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will be [2023]

Q 13 :

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be: [2023]

Q 14 :

Different combination of 3 resistors of equal resistance R are shown in the figures.

The increasing order for power dissipation is: [2023]

0%

0%

Q 17 :

The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1 $Ω$ is connected across these points is __________ J. [2026]

0%

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