(a) In a series LCR circuit connected across an AC source of varible frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the AC source.
(b) What is the phase differene between the voltages across inductor and the capacitor at resonance in the LCR circuit ?
(c ) When and inductor is connected to a 200 V DC voltage, a current of 1Aflows trough it. when the same inductor is connected to a 200 V, 50 Hz AC source, only 0.5 A current flows. Explain, why ? Also, calculate the self inductance of the inductor.

Explanation

(iii) Inductor will offer an additional impedance to ac due to its self-inductance.
Now R = `(V_(rms))/(I_(rms)) = (200)/(1) = 200 Omega`
Impedance of the inductor
`Z = (V_(rms))/(I_(rms)) = (200)/(0.5) = 400 Omega`
Now Z = `sqrt(R^(2) + X_(L)^(2)), ` therefore
`X_(L) = ( sqrt((400)^(2) - (200)^(2)) )` = 346.4`Omega`
Hence inductance (L) is
` L = (X_(L))/(omega) = (346.4)/(2 xx 3.14 xx 50) = 6.2 `H