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

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