Question

Consider two arrangements of $N$ identical resistors, one in parallel and the other in series. Each of these arrangements are connected to batteries of the same voltage. The ratio of power dissipated in the parallel arrangement to the series arrangement is

• A. $N$
• B. $\frac{1}{N}$
• C. $N^2$
• D. $\frac{1}{N^2}$

Answer 1

The correct option is C $N^2$

Let the resistance of each identical resistor be $R$.

For $N$ resistors in parallel, total resistance
$R_p=\frac{R}{N}$

For $N$ resistors in series, total resistance
$R_s=NR$

For same voltage of cell, ratio of powers dissipated
$\frac{P_p}{P_s}=\frac{V^2}{R_p}\times \frac{R_s}{V^2}$
$=\frac{R_s}{R_p}=\frac{NR}{R/N}=N^2$