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 bea)Pb)3Pc)P/3d)2P/3Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Power in a Single Resistor
When a voltage V is applied across a resistance R, the power dissipated in the resistance can be calculated using the formula:

P = (V^2) / R

Here, P represents the power, V is the voltage, and R is the resistance.

Parallel Combination of Resistors
When the same voltage V is applied across a parallel combination of three equal resistors (each of resistance R), the total resistance of the combination can be calculated as:

1/Rt = 1/R + 1/R + 1/R
Rt = R/3

Since the voltage V is the same across all three resistors, the current flowing through each resistor is also the same. Let this current be denoted as I.

Power in Parallel Combination
The power dissipated in each resistor of the parallel combination can be calculated using the formula:

P' = (V^2) / Rt

Substituting the value of Rt, we get:

P' = (V^2) / (R/3)
P' = 3(V^2) / R

Comparison of Power Dissipation
Comparing the power dissipation in the single resistor (P) and the parallel combination of resistors (P'), we can see that:

P' = 3P

Therefore, the power dissipated in the second case (parallel combination) is three times the power dissipated in the first case (single resistor).

Hence, the correct answer is option 'B', 3P.

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