Three resistors, each of resistance R, are arranged in the following different combinations with a source of emf E. Arrange them in the decreasing order of power dissipation:
(A) Three resistors in series
(B) Three resistors in parallel
(C) One resistor in series with two resistors in parallel
(D) One resistor in parallel with two resistors in series
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B), (D), (C), (A)
Power dissipated: $P = \frac{V^2}{R_\text{eq}}$, where $R_\text{eq}$ is the equivalent resistance.
Equivalent resistances:
- (A) Series: $R_\text{eq} = R + R + R = 3R$
- (B) Parallel: $R_\text{eq} = \frac{R}{3}$
- (C) One series with two in parallel: $R_\text{eq} = R + \frac{R \cdot R}{R+R} = R + \frac{R^2}{2R} = R + \frac{R}{2} = \frac{3R}{2}$
- (D) One parallel with two in series: $R_\text{eq} = \frac{1}{\frac{1}{R} + \frac{1}{2R}} = \frac{1}{\frac{3}{2R}} = \frac{2R}{3}$
Power ∝ $1/R_\text{eq}$. Therefore, decreasing order of power dissipation:
$B (R/3) > D (2R/3) > C (3R/2) > A (3R)$