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 A. P B. 3P C. P/3 D. 2p/ 3

The correct answer is $\boxed{\text{C. }P/3}$.

When a voltage $V$ is applied across a resistance $R$, the power dissipated in the resistance is given by $P = V^2/R$.

When the same voltage $V$ is

applied across a parallel combination of three equal resistors each of resistance $R$, the equivalent resistance of the combination is $R_P = R/3$. The power dissipated in each resistor is $P = V^2/(3R)$, and the total power dissipated in the combination is $P_T = 3P = V^2/R$. Therefore, the power dissipated in the second case is $\boxed{\text{C. }P/3}$ of the power dissipated in the first case.

Here is a more detailed explanation of each option:

• Option A: $P$. This is the power dissipated in the first case.
• Option B: $3P$. This is the power dissipated in each resistor in the second case. However, there are three resistors in parallel, so the total power dissipated in the second case is $3P \times 3 = 9P$, which is greater than the power dissipated in the first case.
• Option C: $P/3$. This is the correct answer.
• Option D: $2P/3$. This is the power dissipated in each resistor in the second case if the resistors are connected in series. However, the resistors are connected in parallel, so the total power dissipated in the second case is $2P/3 \times 3 = 2P$, which is greater than the power dissipated in the first case.