Question

Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1.What is the ratio Uc1/Uc2.

Answer 1

Answer:

1/2

Explanation:

The energy stored in a capacitor is given by:

$U=\frac{1}{2}CV^2$

where

C is the capacitance

V is the potential difference

For capacitor 1, we have

$U_1=\frac{1}{2}C_1V_1^2$

Capacitor 2 has

$C_2 = \frac{C_1}{2}$ (half the capacitance of capacitor 1)

$V_2 = 2 V_1$ (twice the potential difference of capacitor 1)

So the energy of capacitor 2 is

$U_2=\frac{1}{2}C_2V_2^2=\frac{1}{2}(\frac{C_1}{2})(2V_1)^2=C_1 V_1^2$

So, the ratio between the two energies is

$\frac{U_1}{U_2}=\frac{\frac{1}{2}C_1 V_1^2}{C_1 V_1^2}=\frac{1}{2}$