Question

The power consumed when 10 V voltage is applied to a series combination of 10 resistors of each 1 \(\Omega\) is \(P_s\), and the power consumed when the same 10 V is applied to the parallel combination of these 10 resistors is \(P_p\). Find the value of \(\frac{P_s}{P_p}\).

• A. 10
• B. 100
• C. 0.1
• D. 0.01

Hint:

For series resistors: \(R_s = \sum R_i\), for parallel: \(1/R_p = \sum 1/R_i\). Power \(P = V^2/R\) to compute ratio.

Answer 1

The Correct Option is D

Step 1: Generalise for n equal resistors.
For $n$ identical resistors $R$, the series combination gives $R_s = nR$ and the parallel combination gives $R_p = R/n$. Since the same voltage is applied in both cases and $P = V^2/R$,
\[ \frac{P_s}{P_p} = \frac{R_p}{R_s} = \frac{R/n}{nR} = \frac{1}{n^2} \]
Step 2: Substitute $n=10$.
\[ \frac{P_s}{P_p} = \frac{1}{10^2} = 0.01 \]
This shortcut skips separately computing $R_s$, $R_p$, $P_s$ and $P_p$.
\[ \boxed{0.01} \]