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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

Step 1: Given

Inductance, L = 0.5H

Resistance, R=100Ω

RMS voltage,Vrms=240v

Frequency, f = 50Hz

Step 2: Calculate impedance for LR circuit

angular frequency, ω=2πf

Substitute values-

ω=2π×50ω=100πrad/s

Inductive reactance, XL=ωL

Substitute values-

XL=100π×0.5XL=50π

Now, the impedance for LR circuit, z=XL2+R2

Substitute values-

z=50π2+1002z=186.142Ω
Step 3: Calculate the Maximum Current In The Circuit

According to ohms law for AC, Vrms=z.Irms, here Irms is the RMS current.

Substitute values-

240=186.142×IrmsIrms=1.289A

Also, Irms=Imax2Imax=Irms2

here Imax is the maximum current.

Substitute values-

Imax=1.2892Imax=1.289×1.414Imax=1.8226A

thus, the The Maximum Current In The Circuit is 1.8226A.

Step 4: Calculate the Time Lag Between Voltage Maximum And Current Maximum

cosϕ=Rzcosϕ=100186.142ϕ=cos-1100186.142ϕ=1radian

now, the time lag, t=ϕωt=1100πs.

Thus, the time lag is 1100πs.

Hence,

(A) The Maximum Current In The Circuit is 1.8226A.

(B) The Time Lag Between Voltage Maximum And Current Maximum is 1100πs.


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