Question

A resistor of resistance R is connected to an ideal battery. If the value of R is decreased, the power dissipated in the resistor will
(a) increase
(b) decrease
(c) remain unchanged

Answer 1

(a) increase

As the resistance is connected to an ideal battery, it provides a constant potential difference across the two terminals. The internal resistance of the battery is also zero.
The power dissipated in the resistor,
P = $\frac{V^2}{R}$

V is constant; hence V $\propto \frac{1}{R^{}}$

Thus, if the value of the resistance is decreased, the power dissipated in the resistor will increase.