n-identical cells, each of emf $\varepsilon,$ internal resistance r connected in series are charged by a dc source of emf $\varepsilon'$ using a resistance R.
- Draw the circuit arrangement.
- Deduce expressions for (a) the charging current and (b) the potential difference across the combination of cells.
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- The circuit arrangement is shown in figure.
Applying Kirchhoff’s second law to the circuit abcda
$-\text{n}\varepsilon-\text{I}(\text{nr)}-\text{IR}+\varepsilon' = 0$
$\Rightarrow\text{I}=\frac{\varepsilon'-\text{n}\epsilon}{\text{R}+\text{nr}}$
- Charging current, $\text{I}=\frac{\epsilon'-\text{n}\varepsilon}{\text{R}+\text{nr}}$
- Potentail difference across the combination V is given by
$\Rightarrow\text{V}=\varepsilon'-\text{IR}$
$\Rightarrow\text{V}=\varepsilon'=\frac{(\varepsilon'-\text{n}\varepsilon)}{\text{R}+\text{nr}}$
$\Rightarrow\text{V}=\frac{\varepsilon'(\text{R}+\text{nr)}-\varepsilon'+\text{n}\varepsilon}{\text{R}+\text{nr}}$
$\Rightarrow\text{V}=\frac{\varepsilon'(\text{R}+\text{nr}-1)+\text{n}\varepsilon}{\text{R}+\text{nr}}$
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