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 \(\frac{P_s}{P_p}\).
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 \(\frac{P_s}{P_p}\).
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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.
Updated On: Jul 18, 2026
- 10
- 100
- 0.1
- 0.01
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The Correct Option is D
Solution and Explanation
Step 1: Compute equivalent resistance in series.
10 resistors each \(R = 1 \, \Omega\) in series:
\[ R_s = 10 \times 1 = 10 \, \Omega \]
Step 2: Compute power in series.
\[ P_s = \frac{V^2}{R_s} = \frac{10^2}{10} = 10 \, \text{W} \]
Step 3: Compute equivalent resistance in parallel.
10 resistors each \(1 \, \Omega\) in parallel:
\[ \frac{1}{R_p} = 10 \cdot \frac{1}{1} = 10 \implies R_p = 0.1 \, \Omega \]
Step 4: Compute power in parallel.
\[ P_p = \frac{V^2}{R_p} = \frac{10^2}{0.1} = 1000 \, \text{W} \]
Step 5: Compute ratio.
\[ \frac{P_s}{P_p} = \frac{10}{1000} = 0.01 \]
Step 6: Final conclusion.
Hence, the ratio of power in series to parallel combination is:
\[ \boxed{0.01} \]
10 resistors each \(R = 1 \, \Omega\) in series:
\[ R_s = 10 \times 1 = 10 \, \Omega \]
Step 2: Compute power in series.
\[ P_s = \frac{V^2}{R_s} = \frac{10^2}{10} = 10 \, \text{W} \]
Step 3: Compute equivalent resistance in parallel.
10 resistors each \(1 \, \Omega\) in parallel:
\[ \frac{1}{R_p} = 10 \cdot \frac{1}{1} = 10 \implies R_p = 0.1 \, \Omega \]
Step 4: Compute power in parallel.
\[ P_p = \frac{V^2}{R_p} = \frac{10^2}{0.1} = 1000 \, \text{W} \]
Step 5: Compute ratio.
\[ \frac{P_s}{P_p} = \frac{10}{1000} = 0.01 \]
Step 6: Final conclusion.
Hence, the ratio of power in series to parallel combination is:
\[ \boxed{0.01} \]
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