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Average and Instaneous Power

If R1 and ...

Question

If $R_{1}$ and $R_{2}$ are filament resistances of a 200 W and a 100 W bulb respectively, designed to operate on the same voltage, then:

A

R_{1} = R_{2}

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B

R_{2} = 2 R_{1}

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C

R_{2} = 4 R_{1}

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D

R_{1} = 4 R_{2}

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Solution

The correct option is C $R_{2} = 2 R_{1}$
Power, $P = \frac{V^{2}}{R}$
For first bulb power, $P_{1} = \frac{V_{1}^{2}}{R_{1}}$
For second bulb power, $P_{2} = \frac{V_{2}^{2}}{R_{2}}$
Divide the above equations:
$\frac{P_{1}}{P_{2}} = \frac{V_{1}^{2} \times R_{2}}{V_{2}^{2} \times R_{1}}$
Substitute: $P_{1} = 200 W$ and $P_{2} = 100 W$ and $V_{1} = V_{2}$ (as bulbs operate at same voltage)

$\Rightarrow \frac{200}{100} = \frac{R_{2}}{R_{1}}$

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

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