JEE Advanced 2022 · Paper 2 · Physics Q10

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PhysicsMultiple correct+4 / -2Question 28 of 54

In Circuit-1 and Circuit-2 shown in the figures, $R_1 = 1\ \Omega$ , $R_2 = 2\ \Omega$ and $R_3 = 3\ \Omega$ .
$P_1$ 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?

Circuit-1: from terminal A, R1 in parallel with switch S1 leads to a junction; from the junction, R2 and R3 in series are in parallel with R1/2, and both lead to terminal B. Circuit-2: R1, R2, R3 and a branch of switch S2 in series with 2R3 are all connected in parallel between terminals A and B.

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 Amp 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 Amp is connected across A and B in both circuits,

Q_2 < Q_1

Answer and worked solution

Official answer: A, B, C

Equivalent resistances ( $R_1=1$ , $R_2=2$ , $R_3=3$ Ω).

Circuit-1: $R_1$ $R_{1}$ (shorted when $S_1$ $S_{1}$ closes) is in series with $(R_2+R_3)\parallel\frac{R_1}2=5\parallel0.5=\frac5{11}$ $(R_{2} + R_{3}) ∥ \frac{R _{1}}{2} = 5 ∥ 0.5 = \frac{5}{11}$ Ω.
- $S_1$ open: $\frac{16}{11}\approx1.455$ Ω.
- $S_1$ closed: $\frac5{11}\approx0.455$ Ω.
Circuit-2: $R_1,R_2,R_3$ $R_{1}, R_{2}, R_{3}$ in parallel, plus $2R_3=6$ $2 R_{3} = 6$ Ω when $S_2$ $S_{2}$ closes.
- $S_2$ open: $\frac6{11}\approx0.545$ Ω.
- $S_2$ closed: $\left(1+\frac12+\frac13+\frac16\right)^{-1}=0.5$ Ω.

Powers. A voltage source gives $V^2/R$ ; a current source gives $I^2R$ .

(A) 6 V: $P_1=\frac{36}{1.455}=24.75$ W and $P_2=66$ W, so $P_1<P_2$ . True.
(B) 2 A: $P_1=4(1.455)=5.82$ W and $P_2=2.18$ W, so $P_1>P_2$ . True.
(C) 6 V: $Q_1=\frac{36}{0.455}=79.2$ W, which is more than $P_1$ . True.
(D) 2 A: $Q_2=4(0.5)=2$ W and $Q_1=1.82$ W, so $Q_2>Q_1$ . False.

(A), (B), (C).

Topics:Electrical power and heating Series and parallel resistors

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JEE Advanced 2022 · Paper 2, Physics question 10