|Class 12 Physics Alternating Current||Phasor diagram for Series LCR circuit|
Phasor diagram for Series LCR circuit
(a) Relation between the phasors VL, VR, VC, and I,
(b) Relation between the phasors VL, VR, and (VL + VC) for the circuit.
(a) Phasor diagram of V and I.
(b) Graphs of v and i versus w t for a series LCR circuit where XC > XL.
Problem:- A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which R = 3 W, L = 25.48 mH, and C = 796 μF.
Find (a) the impedance of the circuit; (b) the phase difference between the voltage across the source and the current; (c) the power dissipated in the circuit; and (d) the power factor.
(a) To find the impedance of the circuit, we first calculate XL and XC.
XL = 2 π ν L
= 2 × 3.14 × 50 × 25.48 × 10–3 W = 8 W
XC = (1/2 π ν C)
= (1/ 2 × 3.14 × 50 × 796 x 10-6)
Z = √R2 + (XL − XC )2 =√(3)2 + (8 − 4)2
= 5 Ω
(b) Phase difference, f = tan–1 ϕ (XC – XL)/(R)
Since ϕ is negative, the current in the circuit lags the voltage across the source.
(c) The power dissipated in the circuit is
P2 = I R
Now, I = (IM)/(√2)
Therefore, P = (40A )2× 3W = 4800
(d) Power factor = cos ϕ = cos53.1° = 0.6