Question

If n resistor of r ohm each are connected first in series than in parallel across same potential difference. calculate the ratio of power decipated in series to that in parallel.

Answer 1

Dear Student
Power depends on voltage across the circuit and resistance of the circuit
$$\begin{gathered} P=\frac{V}{R} \\ {P}_{sereis}=\frac{V}{r+r+r+.....+r_n}=\frac{V}{nr} \\ {P}_{parallel}=\frac{V}{R_{prallel}}=V\left(\frac{1}{r}+\frac{1}{r}+...\frac{1}{r_n}\right)=\frac{Vn}{r} \\ \frac{P_{sereis}}{P_{parallel}}=\frac{\frac{V}{nr}}{\frac{Vn}{r}}=\frac{1}{n^2} \end{gathered}$$

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