Question:
A 300V battery is connected across capacitors of 3uF and 6µF in parallel.
Calculate the energy stored in each capacitor.
Solution
Given,
Potential $V = 300\;V$
Capacitor $C_1 = 3\mu F$
Capacitor $C_2 = 6\mu F$
Energy stored in each capacitor $E = ?$
When the capacitors are connected in parallel, then the equivalent capacitance
$C = C_1 + C_2 = (3 + 6)\;\mu F = 9 \; \mu F$
We have,
Energy stored in a capacitor ($C_1$);
$E_1 = \frac{1}{2}C\;V^2 = \frac{1}{2} * 3 * 10^{-6} * 300^2 = 0.135\;J$ Energy stored in a capacitor ($C_2$);
$E_2 = \frac{1}{2}C\;V^2 = \frac{1}{2} * 6 * 10^{-6} * 300^2 = 0.27\;J$ Energy stored in the equivalence capacitance ($C$);
$E = \frac{1}{2}C\;V^2 = \frac{1}{2} * 9 * 10^{-6} * 300^2 = 0.405\;J$
Potential $V = 300\;V$
Capacitor $C_1 = 3\mu F$
Capacitor $C_2 = 6\mu F$
Energy stored in each capacitor $E = ?$
When the capacitors are connected in parallel, then the equivalent capacitance
$C = C_1 + C_2 = (3 + 6)\;\mu F = 9 \; \mu F$
We have,
Energy stored in a capacitor ($C_1$);
$E_1 = \frac{1}{2}C\;V^2 = \frac{1}{2} * 3 * 10^{-6} * 300^2 = 0.135\;J$ Energy stored in a capacitor ($C_2$);
$E_2 = \frac{1}{2}C\;V^2 = \frac{1}{2} * 6 * 10^{-6} * 300^2 = 0.27\;J$ Energy stored in the equivalence capacitance ($C$);
$E = \frac{1}{2}C\;V^2 = \frac{1}{2} * 9 * 10^{-6} * 300^2 = 0.405\;J$