A 50 Hz AC current of peak value 2 A flows through one of the pair of coils. If the mutual inductance between the pair of coils is 150 mH, then the peak value of voltage induced in the second coil is

Options

A. `30 piV`
B. `60 pi V`
C. `15 pi V`
D. `300 piV`

Answer

A

Explanation

`M = 150 xx 10^(-3)H`
`i = 2A`
f = 50 Hz
Induced voltage,
`e = (d phi)/(d t)`
`= (d)/(d t)(M i) = (d)/(dt)(Mi_(0) sin omega t) = Mi_(0) omega cos omega t`
e is maximum when `cos omega t = 1`
`therefore e= Mi_(0) omega`
`= 150 xx 10^(-3) xx i xx 2 pi f`
`= 150 xx 10^(-3) xx 2 xx 2pi xx 50`
`= 30 pi V`