Question

Consider an RLC series circuit with R = 600 Ω, L = 3 H, C = 4μF, generator voltage V = 20 v, frequency= 60 hz.

Find

a) the inductive impedance X_L,

b) capacitive impedance X_{c ,}

c) Total impedance Z,

d) Line current I ,

e) Voltage drops V_R , V_L, ,V_c

f) combination voltage V_RL , and V_Lc ,

g) phase angle φ ,

h) resonant frequency f₀ ,

i) Power dissipated by circuit.

Answer 1

Giveno- R=gooch L = 3H C = 4uF = 4x166F V - 20 Volt f = 60 Hz We know that, Angular frequency (W) = 217f - 2x Tx60 = 376.993 377 radis (a) Inductive impedance (XL) – XL = WL = 377 *3 XL = 1131 2 ANS (5) Capacitive impedance ( Xc) – - Xc = wC 377x4x106 Xc = 663.13 u ANS (C) Total Impedance (2)- Za R^4(x -x.)* (600)²+(1131– 663.13)2 Z = 760.86 2 ANS

(d) Line Current (i) - ė = V z = 20 760.06 i = 0.0263 A ANS (e) Voltage Drops- è R V "R = 0.0263x600 VR = 15.78 V. ANS V i XL = 0.0263~1131 V. 2 = = 29.75 V ANS Vc = exe = 0.0263 x 663:13 ANS Vc 17.44V (f) Combination voltage. URL and Ve. URL ph VRL + V² 96 Ve+ (15-70)+(29.75)2 Phase diagram. VRL= 33.67 volt! ANS

VL P(VL-Vc) And Kc = "- Ve = 29.75-17.44 Vc Vis = 12-31 Volt/ ANS Phase diagram 19) Phase angle (0) VL-Ve VR 29.75-17.44 15.70 tano (V-V) = Ve = Phase Diagram tant (0.78) क = 37.96 ANS Ch Resonant frequency (fo) – In the case of Resonance → XL = Xc WL = wl w2 LC (217. f.)² = 16 21 TLC fo - - 20 W 3 x 4x10-6 fo = 45.94 Hz. ANS

lis power dissipated by circuit (P) – P=vx = 20 x 0.0263 Р =0.526 Walt | ANS