A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.

Options

A. `3.3Omega and (1)/(250)s`
B. `3.9kOmega and (1)/(160)s`
C. `4.2kOmega and (1)/(100)s`
D. `2.8kOmega and (1)/(120)s`

Answer

A

Explanation

Given, inductance `L=0.01H`, resistance `R=1Omega`,
voltage V=200 V and frequency `f=50Hz`
Impedance of the circuit
`Z=sqrt(R^(2)+X_(L)^(2))=sqrt(R^(2)+(2pifL)^(2))`
`=sqrt(1^(2)+(2xx3.14xx50xx0.01)^(2))`
`Z=sqrt(10.86)=3.3Omega`
`tan phi=(omegaL)/(R)=(2pifL)/(R)`
`=(2xx3.14xx50xx0.01)/(1)=9.14`
`phi=tan^(-1)(3.14)=72^(@)`
Phase difference `phi=(72xxpi)/(180)` rad
Time lag between alternating voltage and current
`Deltat=(phi)/(omega)=(72pi)/(180xx2pixx50)=(1)/(250)s`