Answer to Question #159152 in Electric Circuits for Nike

Question

A charged capacitor of capacitance C can be discharged through a resistor R. At time t after the discharge has started, the charge Q remaining on the capacitor can be given by the expression:
Q = Qoe^(-t/RC)
(i) State the significance of Qo
(ii) Use this equation to obtain an expression for the half-life T1/2 of the discharge process.

Answer 1

(i) $Q_0$ is the initial value of the charge, that the capacitor has at t = 0, i.e at the moment, when discharge starts.

(ii) The half-life $T_{1/2}$ of the discharge process is the time, what is required for dicreasing of the charge of the capacitor to $\frac{Q_0}{2}$ :

$\frac{Q_0}{2}=Q_0e^{-\frac{T_{1/2}}{RC}},$

$\frac{1}{2}=\frac{1}{e^{\frac{T_{1/2}}{RC}}},$

$e^{\frac{T_{1/2}}{RC}}=2,$

$T_{1/2}=RC\cdot ln2.$