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Parallel Combination of Cells

A cell sends ...

Question

A cell sends a current $i_{1}$ through a coil of resistance $R_{1}$ and a current $i_{2}$ through a coil of resistance is $R_{2}$ .The emf of the cell is

\frac{i_{1} i_{2}}{(i_{1} + i_{2})} (R_{1} + R_{2})

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\frac{i_{1} i_{2}}{(i_{1} - i_{2})} (R_{1} - R_{2})

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\frac{i_{2} R_{2} - i_{1} R_{1}}{i_{1} + i_{2}}

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\frac{i_{2} R_{2} - i_{2} R_{1}}{R_{1} + R_{2}}

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Solution

The correct option is B $\frac{i_{1} i_{2}}{(i_{1} - i_{2})} (R_{1} - R_{2})$
$i_{1} = \frac{E}{R_{1} + r}$
where r is the terminal resistance of the cell.
$r = \frac{E - i_{1} R_{1}}{i_{1}} O r i_{2} = \frac{E}{R_{2} + r}$
Also $E = i_{2} R_{2} + i_{2} r = i_{2} R_{2} + i_{2} (\frac{E - i_{1} R_{1}}{i_{1}})$
Simplifying, we get $E = \frac{i_{1} i_{2} (R_{2} - R_{1})}{i_{1} - i_{2}}$

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