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Question

When resistors R1 and R2 are connected in series across a battery of potential difference V, the power dissipated by the resistors are P1 and P2 respectively. When they are connected in parallel across a battery of potential difference E, the power dissipated is P3 and P4​ respectively. Which one of the following is true?

A
P1:P2=R1:R2
and P3:P4=R1:R2
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B
P1:P2=R2:R1
and P3:P4=R1:R2
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C
P1:P2=R1:R2
and P3:P4=R2:R1
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D
P1:P2=R2:R1
and P3:P4=R2:R1
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Solution

The correct option is C P1:P2=R1:R2
and P3:P4=R2:R1
In a series connection, the current flowing through the resistors is the same. If the current is taken as I, then P1=I2×R1 and P2=I2×R2
Hence,P1:P2=R1:R2.
In a parallel connection, the potential difference across the resistors is the same. Hence, P3=E2/R1 and P4=E2/R2
Hence,P3:P4=R2:R1.

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