A series LCR circuit with R = 20 Ω , L = 5 H , and C = 80 μF is connected to a variable frequency 220 ac supply,. Calculate the impedance and the current at resonance condition.

Given The Inductance of the inductor, L = 5 . 0 H . The capacitance of the capacitor, C = 80 μF = 80 × 10 - 6 F . Resistance of the resistor, R = 20 Ω . Potential of the variable voltage source, V = 220 V . The impedance of the circuit is given by the relation: Z = R 2 + X L - X C 2 , where X L , X C are the impudence of inductive resistance and capacitive resistance respectively. At resonance X L = X C , hence we get, Z = R = 20 Ω ...............................................(A) At resonance, the peak voltage V max = 2 V = 2 × 220 . Therefore, the peak current, I max = V max Z = 2 × 220 20 = 15 . 55 A ........................(B) Hence, at the resonance, the impedance= 20 Ω and current = 15 . 55 A

A series LCR circuit with R = 20 Ω , L = 5 H , and C = 80 μF is connected to a variable frequency 220 Hz supply,. (a) What is the angular frequency ω 0 of the source at which resonance occurs?

Given The Inductance of the inductor, L = 5 . 0 H . The capacitance of the capacitor, C = 80 μF = 80 × 10 - 6 F . Resistance of the resistor, R = 20 Ω . Potential of the variable voltage source, V = 220 V . The resonance angular frequency is given as: ω r = 1 LC = 1 5 . 0 × 80 × 10 - 6 = 50 rad / s . Hence, the circuit will come in resonance for a source frequency of 50 rad / s .