In Circuit-1 and Circuit-2 shown in the figures, , and . and are the power dissipations in Circuit-1 and Circuit-2 when the switches and are in open conditions, respectively. and are the power dissipations in Circuit-1 and Circuit-2 when the swit

Question

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]

Smart Achievers · Accepted Answer

(3, 4)

When both switches are open

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

$P_{1}$

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

$S_{2}$

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

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

Solution

1 When a voltage source of 6 V is connected across A and B in both circuits, $P_{1} < P_{2}$ .

2 When a constant current source of 2 $A m p$ is connected across A and B in both circuits, $P_{1} > P_{2}$ .

3 When a voltage source of 6 V is connected across A and B in Circuit-1, $Q_{1} > P_{1}$ .

4 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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Solution

1 When a voltage source of 6 V is connected across A and B in both circuits, P1<P2.

2 When a constant current source of 2 Amp is connected across A and B in both circuits, P1>P2.

3 When a voltage source of 6 V is connected across A and B in Circuit-1, Q1>P1.

4 When a constant current source of 2 Amp is connected across A and B in both circuits, Q2<Q1.

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1 When a voltage source of 6 V is connected across A and B in both circuits, $P_{1} < P_{2}$ .

2 When a constant current source of 2 $A m p$ is connected across A and B in both circuits, $P_{1} > P_{2}$ .

3 When a voltage source of 6 V is connected across A and B in Circuit-1, $Q_{1} > P_{1}$ .

4 When a constant current source of $2 A m p$ is connected across A and B in both circuits, $Q_{2} < Q_{1}$ .