In a series LCR circuit with an AC source, R = 300Ω, C = 20 μF, L = 1.0 Henry, ϵ_rms = 50 V and v = 50/π Hz. Find
(a) The rms current in the circuit and

(b) The rms potential differences across the capacitor, the resistor and the inductor. Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source.

Question

Philoid · Accepted Answer

Given: resistance R = 300Ω,

Capacitance of capacitor C = 20 μF,

Inductance of inductor L = 1.0 Henry,

Voltage across the circuit ϵ_rms = 50 V and

Frequency v = 50/π Hz

{a} rms current in the circuit will be

Where Z is impedance in the circuit

Then,

{b} potential difference across the capacitor will be

Potential difference across the resistor will be

Potential difference across the inductor will be

Net sum of all potential drops =

Rms voltage,

Hence, sum of all potential drops > rms potential applied.