Answer to Question #291430 in Electric Circuits for Zee

Question

A 1000mf capacitor is charged to 10v and 16uf capacitor is charged to 400v.these are then connected in parallel with plates carrying similar charges connected together. Determined the total stored energy before and after joining them. Is final energy the same as the initial energy?

Answer 1

Energy stored in capacitor

$E= ½CV^2$

Energy before connection $=\frac{1}{2}×1000×10^{-3}×10^2+\frac{1}{2}×16×10^{-6}×400^2$

$=51.28J$

After connection

$C_T=C_1+C_2$

Total capacitance$=1000×10^{-3}+16×10^{-6}$

$=1.000016$

Charge on capacitor

$Q=CV$

Total charge

$=1000×10^{-3}×10+16×10^{-6}×400$

$=10.0064$

$E=½CV^2$

But $V=\frac {Q}V$

$E=\frac{Q^2}{2C}$

Energy after connection

$=\frac{1}{2}×\frac{10.0064^2}{1.000016}$

$=50.0632$

Energy is not conserved

Some of if is converted into heat in the connecting wires.