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Ohm's Law

When 2 resist...

Question

When $2$ resistors are in parallel combination then determine $i_{1}$ and $i_{2}$ , if the combination carries a current $i$ ?

i_{1} = \frac{i R_{2}}{R_{1}}

and

i_{2} = \frac{i R_{1}}{R_{2}}

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i_{1} = \frac{i R_{2}}{R_{1} + R_{2}}

and

i_{2} = \frac{i R_{1}}{R_{1} + R_{2}}

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i_{1} = \frac{i R_{1}}{R_{1} + R_{2}}

and

i_{2} = \frac{i R_{2}}{R_{1} + R_{2}}

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Solution

The correct option is B $i_{1} = \frac{i R_{2}}{R_{1} + R_{2}}$ and $i_{2} = \frac{i R_{1}}{R_{1} + R_{2}}$
Since, $R_{1}$ and $R_{2}$ are in parallel, so potential difference across them will be same.
$∴ i_{1} R_{1} = i_{2} R_{2}$

$\Rightarrow \frac{i_{1}}{i_{2}} = \frac{R_{2}}{R_{1}}$

$\Rightarrow \frac{i_{1} + i_{2}}{i_{2}} = \frac{R_{2} + R_{2}}{R_{1}}$

Given: $i = i_{1} + i_{2}$

$∴ \frac{i}{i_{2}} = \frac{R_{2} + R_{2}}{R_{1}}$

$\Rightarrow i_{2} = \frac{R_{1} i}{R_{1} + R_{2}}$

Similarly,

$i_{1} = \frac{R_{2} i}{R_{1} + R_{2}}$

Hence, option $(a)$ is correct.

Why this question?
Note:Remember this law of $i \propto \frac{1}{R}$ in the resistor connected in parallel. It can be used in problems.

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Ohm's Law

Standard X Physics

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When 2 resistors are in parallel combination then determine i1 and i2, if the combination carries a current i ?

When $2$ resistors are in parallel combination then determine $i_{1}$ and $i_{2}$ , if the combination carries a current $i$ ?