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Combination of Resistors

When resistor...

Question

When resistors $R_{1} a n d R_{2}$ are connected in series across a battery of potential difference V, the power dissipated by the resistors are $P_{1} a n d P_{2}$ respectively. When they are connected in parallel across a battery of potential difference E, the power dissipated is $P_{3} a n d P_{4}$ 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 $P_{1} = I^{2} \times R_{1} a n d P_{2} = I^{2} \times R_{2}$
$H e n c e, P_{1} : P_{2} = R_{1} : R_{2}$ .
In a parallel connection, the potential difference across the resistors is the same. Hence, $P_{3} = E^{2} / R_{1} a n d P_{4} = E^{2} / R_{2}$
$H e n c e, P_{3} : P_{4} = R_{2} : R_{1}$ .

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