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

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.
• Find the maximum energy stored in the inductance.

Solution
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