Given:

Coil resistance = 0 (approx)

L= 0.2H; VS = 150 V; f= 50Hz

To Find: i(t), v(t)

Step 1: Time equation for voltage

$X_L=2π\times50\times0.2=62.83 \ Ω \\[2ex] V_{rms}=150 \ V \\[2ex] ∴v(t)=V_m sin⁡ωt=212.13 \ sin⁡(100πt) \ Volt $

Step 2: Time equation for current

Peak current

$I_m=\dfrac{V_m}{X_L} =\dfrac{212.13}{62.83}=3.83 \ Amp$

Due to purely inductive voltage, the current will lag behind voltage by 90° or by (π/2) radians.

$i(t)=3.38 sin \displaystyle{(100πt-\dfrac{π}2)} Amp$