Question

Two identical cells are first connected in series and then in parallel. The ratio of power consumed by them is

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:4$

Answer 1

Answer: (A)

Let emf of a cell $=\epsilon$
and its internal resistance $=r$
Power consumed by any resistance $R$ is given by
$P=\frac{V^2}{R}$
For series combination,
$V=2\epsilon$ and $R=2r$
$\therefore P_s=\frac{(2\epsilon {)}^2}{2r}=\frac{2{\epsilon }^2}{r}$
For parallel combination, $V=\epsilon$ and $R=\frac{r}{2}$
$\therefore P_p=\frac{{\epsilon }^2}{\frac{r}{2}}=\frac{2{\epsilon }^2}{r}$
Hence, $\frac{P_s}{P_p}=\frac{2{\epsilon }^2}{r}\times \frac{r}{2{\epsilon }_{{}^2}}=\frac{1}{1}$