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(B) The resistance $R$ of an electrical appliance is given by the formula $R = \frac{V^2}{P}$,where $V$ is the voltage and $P$ is the power rating.Ass

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$25 \, W$ bulb,$2$ times

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(B) The resistance $R$ of an electrical appliance is given by the formula $R = \frac{V^2}{P}$,where $V$ is the voltage and $P$ is the power rating.Assuming the voltage $V$ remains constant for both bulbs,the relationship between resistance and power is inversely proportional,i.e.,$R \propto \frac{1}{P}$.For a $50 \, W$ bulb: $R_1 = \frac{V^2}{50}$.For a $25 \, W$ bulb: $R_2 = \frac{V^2}{25}$.Comparing the two: $\frac{R_2}{R_1} = \frac{V^2/25}{V^2/50} = \frac{50}{25} = 2$.Therefore,the $25 \, W$ lamp has double ($2$ times) the resistance of the $50 \, W$ lamp.

State which has a higher resistance,a $50 \, W$ or a $25 \, W$ lamp bulb,and by how many times?

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