Question

A 1500uF capacitor is fully charged using a 100V DC supply. It is disconnected from the power and connected to an uncharged 1000uF capacitor.
(i) Calculate the PD across the terminals of each capacitor
(ii) Calculate the initial and final energies stored in the capacitors hence explain why there is a loss in energy?

Answer 1

Answer

Total charge on 1500$\mu F$ capacitor

$Q=CV\\=0.0015\times100\\Q=0.15columb$

When supply is disconnected and another capacitor is connected then

Voltage across each capacitor

$V_1=\frac{0.15}{0.0015+0.0010}=60volts$

(ii) initial energy stored

$U_i=\frac{1}{2}CV^2=\frac{1}{2}(0.0015)(100)^2\\U_i=7.5J$

Final energy

$U_f=\frac{1}{2}C_{eq}V_1^2\\=\frac{1}{2}(0.0015+0.0010)(60)^2=4.5J$

Loss in energy =$U_i-U_f=7.5-4.5\\=3J$