Suppose voltage V is applied across a resistance R. The power dissipat

Suppose voltage V is applied across a resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case will be

P
3P
P/3
2P/3
This question was previously asked in
UPSC CDS-1 – 2017
The correct answer is B) 3P.
In the first case, power dissipated is P = V²/R.
In the second case, three equal resistors, each of resistance R, are connected in parallel across the same voltage V. The equivalent resistance of three resistors in parallel is R_eq = 1 / (1/R + 1/R + 1/R) = 1 / (3/R) = R/3.
The power dissipated in the second case is P’ = V²/R_eq. Substituting R_eq = R/3, we get P’ = V²/(R/3) = 3 * (V²/R).
Since P = V²/R, the power dissipated in the second case is P’ = 3P.
When resistors are connected in parallel across a constant voltage source, the total power dissipated is the sum of the power dissipated in each resistor. In this case, each of the three resistors R has voltage V across it, so each dissipates power P = V²/R. The total power is P + P + P = 3P. Using the equivalent resistance method confirms this result.