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?

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A wire when connected to 220V mains supply has power dissipation P1. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in the case is P2. The ratio of P2:P1 is

The correct option is B 4P=v2RR=ρlA∴P=v2ρl.A∴P1=v2.AρlNow,R2=R2=ρ(12)A.2=ρ.l4A∴P2=v2ρl.4A=4P1∴P2P1=4

A wire when connected to 220V mains supply has power dissipation $P_{1}$ . Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in the case is $P_{2}$ . The ratio of $P_{2} : P_{1}$ is

The correct option is B 4
$P = \frac{v^{2}}{R} R = \frac{ρ l}{A} ∴ P = \frac{v^{2}}{ρ l} . A ∴ P_{1} = \frac{v^{2} . A}{ρ l} N o w, R^{2} = \frac{R}{2} = \frac{ρ (\frac{1}{2})}{A .2} = \frac{ρ . l}{4 A} ∴ P_{2} = \frac{v^{2}}{ρ l} . 4 A = 4 P_{1} ∴ \frac{P_{2}}{P_{1}} = 4$