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Electric Power

When resistor...

Question

When resistors $R_{1}$ and $R_{2}$ are connected in series across a battery of potential difference $V,$ the power dissipated by the resistors are $P_{1}$ and $P_{2}$ respectively. When they are connected in parallel across a battery of potential difference $E,$ the power dissipated is $P_{3}$ and $P_{4}$ respectively. Which one of the following is true?

A

P_{1} : P_{2} = R_{1} : R_{2} . a n d P_{3} : P_{4} = R_{1} : R_{2}

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B

P_{1} : P_{2} = R_{2} : R_{1} a n d P_{3} : P_{4} = R_{1} : R_{2}

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C

P_{1} : P_{2} = R_{1} : R_{2} a n d P_{3} : P_{4} = R_{2} : R_{1}

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D

P_{1} : P_{2} = R_{2} : R_{1} a n d P_{3} : P_{4} = R_{2} : R_{1}

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Solution

The correct option is C $P_{1} : P_{2} = R_{1} : R_{2} a n d P_{3} : P_{4} = R_{2} : R_{1}$
In a series connection, the current flowing through the resistors is the same. If the current is taken as $I,$ then $P_{1} = I^{2} \times R_{1}$ and $P_{2} = I^{2} \times R_{2}$
Hence, $P_{1} : P_{2} = R_{1} : R_{2}$ .
In a parallel connection, the potential difference across the resistors is the same. Hence, $P_{3} = \frac{E^{2}}{R_{1}}$ and $P_{4} = \frac{E^{2}}{R_{2}}$
Hence, $P_{3} : P_{4} = R_{2} : R_{1}$ .

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