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Two bulbs of (40 W, 200 V) and (100 W, 200 V). Then correct relation for their resistance :
A
$R_{40} \lt R_{100}$
B
$R_{40} \gt R_{100}$
C
$R_{40} = R_{100}$
D
No relation can be predicted
Detailed Solution
$P = \dfrac{V^2}{R}$; for the same rated voltage, $P \propto \dfrac{1}{R}$.
$R_{40} = \dfrac{200^2}{40} = 1000\ \Omega$ and $R_{100} = \dfrac{200^2}{100} = 400\ \Omega$
So the bulb of lower power has the higher resistance: $R_{40} \gt R_{100}$.
$R_{40} = \dfrac{200^2}{40} = 1000\ \Omega$ and $R_{100} = \dfrac{200^2}{100} = 400\ \Omega$
So the bulb of lower power has the higher resistance: $R_{40} \gt R_{100}$.