Question

A current is flowing in a circuit consisting of a resistor and a battery.
What happens to the power dissipated in the resistor when the resistance is quadrupled and the voltage remains constant?

• A. It is doubled
• B. It is quadrupled
• C. It is halved
• D. It is quartered
• E. It remains the same

Answer 1

Answer: (D)

Let the voltage of the battery be $V$ and initial resistance be $R$.

Thus, the initial power dissipated is $P=\frac{V^2}{R}$

Now the resistance is quadrupled keeping the voltage constant i.e $R^{\prime }=4R$

$\therefore$ New power dissipattion is $P^{\prime }=\frac{V^2}{R^{\prime }}=\frac{V^2}{4R}=\frac{P}{4}$

Hence the power dissipated is quartered.