Question

A battery is used to charge a parallel plate capacitor till it becomes fully charged. If capacitance is $C$ and EMF of battery is $\in$, find average current from $t=0$ to $t=RC$. ($R$ = resistance of circuit)

• A. $\frac{0.5\in }{R}$
• B. $\frac{0.63\in }{R}$
• C. $\frac{\in }{R}$
• D. $\frac{0.37\in }{R}$

Answer 1

The correct option is B $\frac{0.63\in }{R}$

$q=C\in (1-e^{-t/RC})$
$q_i=0$
$q_f=C\in (1-e^{-RC/RC})=C\in (1-e^{-1})$

$\Delta q=q_f-q_i=q_f-0=C\in (1-\frac{1}{e})=0.63C\in$

$I=\frac{\Delta q}{\Delta t}=\frac{0.63\text{/}C\in }{R\text{/}C}=\frac{0.63\in }{R}$