Equation of emf of a generator is `V = 282 sin 100 pi t` volt. Internal resistance of generator is `2000 Omega`. It is connected as shown in Fig. Find the frequency of generator and impedance of circuit.

Explanation

Here, `V = 282 sin 100 pi t, R = 2000 Omega`
`L = (40)/(pi) H` and `C = (10)/(pi) mu F . V = ? , Z = ?`
The standard form of alternating emf is
`E = E_(0) sin omega t`. Compare it with
`V = 282 sin 100 pi t`, to get
`E_(0) = 282 V, omega = 2 pi v = 100 pi`,
`v = (100)/(2) = 50 Hz`
`X_(L) = omega L = 2 pi v xx (4)/(pi)`
`= 2 xx 50 xx 40 = 4000 ohm`
`X_(C ) = (1)/(omega C) = (1)/(2 pi v C)`
`(1)/(2 pi xx 50 xx (10)/(pi) xx 10^(-6)) = 1000 Omega`
`Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2))`
`= sqrt((2000)^(2) + (4000 + 1000)^(2))`
`= 10^(3) sqrt( 4 + 9) = 3.6 xx 10^(3) Omega`