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Series Combination of Cells

Two cells of ...

Question

Two cells of emf $2 E$ and $E$ with internal resistance $r_{1}$ and $r_{2}$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R$ , at which the potential difference across the terminals of the first cell becomes zero is

A

r_{1} - r_{2}

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B

r_{1} + r_{2}

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C

\frac{r_{1}}{2} + r_{2}

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D

\frac{r_{1}}{2} - r_{2}

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Solution

The correct option is D $\frac{r_{1}}{2} - r_{2}$

Current in the circuit, $i = \frac{3 E}{R + r_{1} + r_{2}}$

If potential difference across terminals of first cell is zero.

Then, $V_{A} - V_{B} = 0$

$\Rightarrow 2 E - i r_{1} = 0$

$\Rightarrow 2 E = \frac{3 E}{R + r_{1} + r_{2}} r_{1}$

$\Rightarrow 2 R + 2 r_{1} + 2 r_{2} = 3 r_{1}$

$∴ R = \frac{r_{1}}{2} - r_{2}$

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