1.

A coil of inductance 0.50 H and resistance 100 ohm is connected to 240 V, 50 Hz a.c. supply. (a) What is the peak current in the coil ? (b) What is the time lag between the peak voltage and the peak current ?

Answer»

Solution :Here `L = 0.50 H, R = 100` ohm,
`E_(rms) = 240 V, v = 50 Hz`
Step I :
We know
`E_(0) = sqrt(2) E_(rms) = 1.414 XX 240 = 339.4 V`
Impedance of LR circuit is
`Z_(L) = sqrt(R^(2) + omega^(2)L^(2)) = sqrt(R^(2) + 4PI^(2)v^(2)L^(2))`
`= sqrt((100)^(2) + 4 xx (3.14)^(2) xx (50)^(2) xx (0.50)^(2)) = 186.1` ohm
Peak current, `I_(0) = (E_(0))/(Z_(L)) = (339.4)/(186.1) = 1.82 A`
In LR circuit the phase difference between current and voltage `phi` is given by
`tan phi = (0.50 xx2 xx 3.14 xx 50)/(100) = 1.57`
`phi = tan^(-1)(1.57) = 57^(@)30. = 57.5^(@)`
`= (57.5 xx pi)/(180) = 0.3194 pi` radians
Here `E = E_(0) sin omega t , E_(0) = E_(rms) sqrt(2)`
`therefore` Time LAG between `E_(0)` and `I_(0)` is given by
`t = (phi)/(omega) = (phi)/(2pi v) = (0.3194 pi)/(2pi xx 50)`
`= 0.003194 s = 3.194 xx 10^(-3)s`.


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