Question

If the potential difference applied to a fixed resistance is doubled, the power dissipated by that resistance

1. Remains the same
2. Doubles
3. Halves
4. Quadruples

Answer 1

The power dissipated by a resistor is 
$P=I^2 R = \frac{V^2}{R}$
where I is the current, V the voltage and R the resistance.

We can see that if the voltage V is doubled and R is kept fixed, the new dissipated power is
$P' = \frac{(2V)^2}{R}= \frac{4V^2}{R}=4 P$
so, it quadruples.