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Question

A coil of inductance 0.5 H and a resistor of resistance 100Ω are connected in series to a 240V,50 Hz supply.(a) Find the maximum current in the circuit(b) What is the time lag between voltage maximum and current maximum?

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Solution

Given that:-Inductance, L=0.5HResistance, R=100ΩRMS voltage, Vrms=240VFrequency, f=50HzNow, angular frequency, ω=2πfω=2π×50=100π rad/sInductive reactance, XL=ωLXL=100π×0.5=50πomegaFormula for impedance for LR circuit;z=√X2L+R2∴z=√(50π)2+(100)2=186.209Ω(a) We know that;vrms=z.Irms ⇒ Ohm's law for ACvrms=zIrms⇒240=186.209×Irms⇒Irms=(240186.209)A=1.2888AAs Irms=(Imax√2)⇒Imax=√2Irms=(√2×1.2888)A=1.8226AMaximum current in the circuit, Imax=1.8226A(b) cosϕ=Rz=(100186.209)⇒ϕ=cos−1(100186.209)=1radianTime lag, t=ϕw=(1100π)sec.

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