Q: An alternating voltage E = 200√2 sin (100t) volt is connected to a 1μF capacitor through an ac ammeter. What will be the reading of the ammeter ?
Sol: Comparing E = 200√2 sin (100 t) with
E = E0 sin ωt ; E0 = 200 √2 V and ω = 100 rad/s
$\large X_C = \frac{1}{\omega C} = \frac{1}{100 \times 10^{-6}} $
= 104 Ω
$\large i_{rms} = \frac{E_{rms}}{X_C} = \frac{E_0}{\sqrt{2} X_C} $
$\large = \frac{200 \sqrt{2} }{\sqrt{2} \times 10^4} $
= 20 mA