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Question

A coil of inductance 0.50 H and resistance 100Ω is connected to a 240 V, 50 Hz ac supply.
(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

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Solution

(a)
Peak velocity V0=2V=339.41
ω=2πf=100π rad/s
Io=VoR2+ω2L2=1.82 A

(b)

The voltage is given as V=Vocosωt

The current is given as I=Iocos(ωtϕ)

ϕ is the phase angle between the voltage and current.

The time lag is given as ϕ/ω.

Now phase angle is given as tanϕ=ωL/R=2π×50×0.5/100=1.57.

So ϕ=tan11.57=57.5o=57.5π/180 radians

time lag is t=ϕ/ω=57.5π/180×2π×50=3.19×103 s


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