JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · Current Electricity

In Circuit-1 and Circuit-2 shown in the figures,

R_{1} = 1Ω, R_{2} = 2Ω

and

R_{3} = 3Ω

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?

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

Answer: (A), (B), (C)

Solution

With the switches open the equivalent resistances are

R_{C_{1}} = \frac{16}{11} Ω

and

R_{C_{2}} = \frac{6}{11} Ω

. For a voltage source

P = V^{2} / R

, so the larger resistance of Circuit-1 dissipates less and

P_{1} < P_{2}

. For a constant-current source

P = I^{2} R

, so the larger resistance dissipates more and

P_{1} > P_{2}

. With the switches closed the resistances drop to

R_{C_{1}}^{'} = \frac{5}{11} Ω

and

R_{C_{2}}^{'} = \frac{1}{2} Ω

; for a

6

V source across Circuit-1 the smaller resistance raises the dissipation, so

Q_{1} > P_{1}

. For a

2

A source

Q_{1} = I^{2} R_{C_{1}}^{'} = 4 \times \frac{5}{11} = \frac{20}{11} \approx 1.82

W while

Q_{2} = 4 \times \frac{1}{2} = 2

W, so

Q_{2} > Q_{1}

and the statement

Q_{2} < Q_{1}

fails.

JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · One or more correct options