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

- The power dissipated in a resistor is:

\[ P = \frac{V^2}{R}. \]

- For \( R \): \( P_1 \propto \frac{1}{R} \), and for \( 3R \): \( P_2 \propto \frac{1}{3R} \).

- The ratio of powers:

\[ \frac{P_1}{P_2} = \frac{3R}{R} = 3 : 1. \]