Question

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:

• A. 1 : 1
• B. 1 : 3
• C. 1 : 27
• D. 3 : 1

Hint:

 For power dissipation in parallel circuits:
• Power is inversely proportional to resistance in parallel arrangements.
• Compare power ratios directly using \(P ∝ 1/R\).

Answer 1

The Correct Option is D

To solve the problem of finding the ratio of thermal energy released in two resistors \( R \) and \( 3R \) connected in parallel in an electric circuit, we need to understand how power dissipated or energy released in resistive components is calculated.

When resistors are connected in parallel, the voltage across each resistor is the same. The power dissipated in a resistor can be determined using the formula:

P = \frac{V^2}{R}

where \( V \) is the voltage across the resistor and \( R \) is the resistance.

Given that the resistors \( R \) and \( 3R \) are in parallel and the voltage across both is \( V \), the power dissipated (thermal energy released per unit time) in each resistor is:

1. For resistor \( R \): P_1 = \frac{V^2}{R}
2. For resistor \( 3R \): P_2 = \frac{V^2}{3R}

To find the ratio of the thermal energy released in these two resistors, we calculate:

\text{Ratio} = \frac{P_1}{P_2} = \frac{\frac{V^2}{R}}{\frac{V^2}{3R}} = \frac{V^2}{R} \times \frac{3R}{V^2} = \frac{3R}{R} = 3

The ratio of thermal energy released in resistors \( R \) and \( 3R \) is therefore 3:1.

This calculation confirms the correct answer as 3 : 1, which matches with option provided in the question.