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Parallel Combination of Cells

A current i r...

Question

A current i reaching at a point in a circuit gets branched and flows through two resistors $R_{1}$ and $R_{2}$ . Then, the current through $R_{1}$ varies as

A

R_{1}

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B

R_{2}

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C

(R_{1} + R_{2})

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D

1 / (R_{1} + R_{2})

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Solution

The correct options are
B $R_{2}$
D $1 / (R_{1} + R_{2})$

Since potential difference across both resistance is same in parallel combination.
Hence $i_{2} R_{1} = i_{1} R_{2}$

$⟹ i_{1} = \frac{R_{1}}{R_{2}} i_{2}$

Now, from Kirchoff's junction law-

$I = i_{1} + i_{2}$

$⟹ \frac{R_{1}}{R_{2}} i_{1} + i_{1} = I$

$⟹ i_{1} = \frac{R_{2}}{R_{1} + R_{2}} I$

$⟹ i_{1} \propto R_{2}$
and

$i_{1} \propto \frac{1}{R_{1} + R_{2}}$

Answer-(B),(D)

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