Question 115: Current Electricity

Question

Two identical cells, when connected either in parallel or in series gives same current in an external resistance $$5 ~\Omega$$. The internal resistance of each cell will be ___________ $$\Omega$$.

Accepted Answer

$\varepsilon_{	ext {series }}=\varepsilon_{1}+\varepsilon_{2}=2 \varepsilon$
$r_{	ext {series }}=r_{1}+r_{2}=2 r$
$i=\frac{2 \varepsilon}{5+2 r}$ ......(1)
$\varepsilon_{	ext {parallel }}=\frac{\frac{\varepsilon_{1}}{r_{1}}+\frac{\varepsilon_{2}}{r_{2}}}{\frac{1}{r_{1}}+\frac{1}{r_{2}}}=\varepsilon$
$ r_{	ext {parallel }}=\frac{r}{2}$
$$
i=\frac{\varepsilon}{\frac{r}{2}+5}
$$ .......(2)
Equating (1) and (2), we get
$\Rightarrow \frac{2 \varepsilon}{2 r+5}=\frac{\varepsilon}{\frac{r}{2}+5}$
$\Rightarrow r+10=2 r+5 $
$\Rightarrow r=5 \Omega$

Current Electricity

Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5 ~\Omega. The internal resistance of each cell will be ___________ \Omega$.

Integer / Numeric Answer Type