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A voltage of 150V, 50Hz is applied to a coil of negligible resistance and inductance 0.2H. Write the time equation for voltage and current.
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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

XL=2π×50×0.2=62.83 Vrms=150 Vv(t)=Vmsinωt=212.13 sin(100πt) Volt

Step 2: Time equation for current

Peak current

Im=VmXL=212.1362.83=3.83 Amp

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

i(t)=3.38sin(100πtπ2)Amp

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