7.13 A coil of inductance 0.50 H and resistance 100 β„¦ 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?

 

Given,

Inductance, 𝐿𝐿 = 0.50 H

Resistance, 𝑅𝑅 = 100 Ω

rms voltage, 𝑉rms = 240 V

frequency, 𝑓 = 50 Hz

(a) The rms current in the coil,

Irms=VrmsXL2+R2

For an inductive circuit,

XL=2π×50Hz×0.5H=157ΩIrms=240V(157Ω)2+(100Ω)2=240V186.1Ω=1.2A

So, The maximum current in the coil

Im=2×Irms=2×1.2A=1.82A

(b) In LR circuit,

 

 If, V=Vmcosωt then, I=Imcos(ωtϕ)

Voltage is maximum at t = 0 whereas, the current is maximum at = πœ™/πœ”,

Therefore, the time lag between the maximum voltage and maximum current = πœ™/πœ”.

 Also, tanϕ=ωLR=2π×50Hz×0.5H100Ω=1.57ϕ=tan11.57=57.5=57.5π180 Timelag =ϕω=57.5π180×2π×50=3.2ms