Different combination of 3 resistors of equal resistance R are shown in the figures. The increasing order for power dissipation is:

Solution

Physics sir · 3 steps

Every circuit gets the same current I, so P = I² R_(eq): more resistance, more power.

1. Same current. Each circuit carries the same current I, so power depends only on the equivalent resistance. Use P = I² R_(eq).

   Circuit	Arrangement	R_(eq)	P = I² R_(eq)
   A	two in parallel, then one in series	R/2 + R = 3R/2	1.5 I² R
   B	two in series, in parallel with one	(2R × R)/(2R + R) = 2R/3	0.67 I² R
   C	all three in parallel	R/3	0.33 I² R, least
   D	all three in series	3R	3 I² R, most

2. Arrange. The resistances go R/3 < 2R/3 < 3R/2 < 3R, which is C, B, A, D. With I fixed, the powers follow the same order.
3. So. P_C < P_B < P_A < P_D, which is option (b).

The idea to keep. First decide what is fixed. If the current is the same, use P = I²R and more resistance gives more power. If the voltage is the same, use P = V²/R and the order flips.

Answer from the NTA final answer key. Solution by PrepWiser.