JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Current Electricity

Different combination of 3 resistors of equal resistance

R

are shown in the figures.
The increasing order for power dissipation is:

Answer: (D)

Solution

Each network is fed by the same current

I

, so the power dissipated is

P = I^{2} R_{eq}

and is largest where the equivalent resistance is largest.

Two resistors in parallel, in series with the third:

R_{A} = \frac{R}{2} + R = \frac{3 R}{2}

.

Two resistors in series, in parallel with the third:

R_{B} = \frac{2 R \cdot R}{2 R + R} = \frac{2 R}{3}

.

All three in parallel:

R_{C} = \frac{R}{3}

.

All three in series:

R_{D} = 3 R

.

Since

R_{C} < R_{B} < R_{A} < R_{D}

, the dissipated powers follow the same order,

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

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option