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# A 4 microfarad capacitor is charged to 400 volts and then its plates are joined through a resistor of resistance 1K¤ the heat produced in the resistor is

Arun Kumar IIT Delhi
7 years ago
Hi
$\\V(t)=V_0e^{-t/RC} \\I(t)=V_0e^{-t/RC}/R \\=>\int_{0}^{\infty}I^2Rdt \\=>\int_{0}^{\infty}R*V_0^2e^{-2t/RC}/R^2dt \\=>\int_{0}^{\infty}V_0^2e^{-2t/RC}/Rdt \\=>\frac{RC*V_0^2}{2*R}*(1-0)=\frac{C*V_0^2}{2}$

Which is same as the energy stored in a capacitor.