L-C-R Circuit
A 2 `mu F` capacitor, 100 `Omega` resistor and 8 H inductor are connected in series with an AC source. What should be the frequency of source for which the current drawn in the circuit is maximum ? If peak value of emf of source is 200 V, find the maximum current, inductive reactance, capacitive reactance, total impedance, peak value of current in the circuit. What is the phase relation between the voltage, across inductor and resistor ? Also, give the phase relation between voltage across inductor and capacitor.

Explanation

Given, capacitance, `C = 2 mu F = 2 xx 10^(-6) F`
Resistance, `R = 100 Omega`
Inductance, L = 8 H
Peak value of voltage, `E_(0) = 200 V`
When frequency of AC source is equal to resonant frequency, then current drawn in the circuit is maximum.
`therefore" "v = v_(r) = (1)/(2pi sqrt(LC)) = (1)/(2 xx 3.14 xx sqrt(8 xx 2 xx 10^(-6)))`
`= (1000)/(8 xx 3.14) = 39.8` Hz
Peak value of current, `I_(0) = (E_(0))/(R) = (200)/(100) = 2A`
`because " "X_(C) = X_(L) = omega L = 2 pi v L`
`= 2 xx 3.14 xx 39.8 xx 8 = 2000 Omega rArr Z = R = 100 Omega`
The voltages across inductor and resistor differ in phase by `90^(@)` and the voltages across inductor and capacitor differ in phase by `180^(@)`.