A coil of inductance `0.50H` and resistance `100 Omega` is connected to a `240V`, `50Hz` ac supply. What are the maximum current in the coil and the time lag between voltage maximum and current maximum?

Explanation

Inductance of the inductor, L=0.50H
Resistance of the resistor ,R=100`Omega`
potential of the supply voltage ,V=240V
Freqeuncy of the supply, v=50Hz
(a) Peack voltage is given as:
`V_(0)=sqrt(2)V`
`=sqrt(2)xx240=339.41V`
Angular frequency of the supply.
`omega =2nv`
`=2nxx50=100n` rad/s
Maximum current in the circuit is given as:
` I_(@)=(V_(@))/(sqrt(R^(2)+omega^(2)L^(2)))`
(b) Equation for voltage is gien as:
`V=V_(0) cos omegat`
Equation for current is given as:
`I_(0)cos(omegat-phi)` ltbgt where,
`phi=` phase difference between voltage and current At time ,t=0,
`V=V_(0)` (voltage is maximum)
For `omegat-phi=0 i.e.,` at time `t=(phi)/(omega)`,
`I=I_(0)` (current is maximum)
Hence , the time lag between maximum voltage and maximum current is `(phi)/(omega)`
Now, phase angle `phi` is given by the relation,
`tan phi=(omegaL)/(R)`
`=(2pixx50xx0.5)/(100)=1.57`
`phi=57.5^(@)=(57.5pi)/(180)` rad
`omegat=(57.5pi)/(180)`
`omega t=(57.5pi)/(180)`
`t= (57 .5)/(180xx2pixx50)`
` = 3.19xx10^(-3)s`
=3.2ms
Hence, the time lag between maximum voltage and maximum current is 3.2 ms.