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# A 60Hz voltage of 280v effective value is impressed on an inductance of 0.356H.Write the time equation for the voltage and the resulting current.

## Write the time equation for the voltage and the resulting current.

Find the maximum energy stored in the inductance.

Solution

Write the time equation for the voltage and the resulting current.

F = 60Hz, V = 280v, L= 0.356H

Time equation for the resulting voltage

V = VoSin2πft

The root mean square voltage, V

V = `Vo/2

Vo = V × 2

280 × 1.4142 = 395.98V

RESULTING VOLTAGE,

V = VoSin2πft

V = 395.8Sin2 ×3.142 × 60 ×t

V = 395.8Sin377t

Io = Vo/XL

LOAD REACTANCE, XL = 2πfL

XL = 2 ×3.142 ×60 ×0.356

XL = 134.25Ω

Io = 395.8/134.23

Io = 2.95A

TIME EQUATION FOR CURRENT,

I = Io sin [wt – π/2]= 2.95sin[377t – π/2]

Find the maximum energy stored in the inductance.

E = ½ LIRAISE TO POWER 2 max

= ½ ×0.356 ×2.95 ×2.95

= 1.55J