Find the total energy of the dissipated resistor In your electronic circuit cour

Question

Find the total energy of the dissipated resistor

In your electronic circuit courses you learned that the power dissipated by current I through resistor R is Power P = I^2 R and that the energy stored on a capacitor C when charged to voltage V_0 volts is equal to 1/2(CV_0^2). In the simple RC circuit shown above, the capacitor is initially charged to a voltage = V_0 volts. After charging the capacitor, a switch is then closed and the capacitor discharges through the resistor R. (a) As you probably know, the discharge rate decreases exponentially as the voltage across the capacitor decreases. The decaying voltage across the resistor at time t is V(t) = V_0(exp[-t/RC]). Find the total energy dissipated in the resistor when the capacitor has fully discharged.

Explanation / Answer

In the above circuit the only componnt to discharge energy is resister. Since the total charge of the capacitor is derived to be 0.5xCxV02. Using conservation of energy priciple the toal energu dissipated by resistor will be the same to energy stored in capacitor i.e 0.5xCxV02 .

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