Question

2) In an RLC circuit, ? = 10 Ω, ? = 0.5 ??, and ? = 6.0 ??, the current in the inductor is ?? = 12 ? sin(?? + 0.2). The circuit operates at half of the resonance frequency.

a) Find the current in the resistor, capacitor and for the entire circuit.

b) Find the voltage in the resistor, capacitor, and inductor.

c) Find the emf of the AC source.

Answer 1

R с L given RLC are in woon series of so current - is same across inductor, resistance and capacitor . v I,= Ic= IR IR = 12 sin (wt +0.2) 12 sin (wt +0.2) Ic= resonance frequency (do) wo= = 27 So SLC fo= > 27 JLC 27 Jo.5x153x6 X100 2.90x103 34.41 giren circuit operates at half of frequency దు 1.45 x 103 2

X = WL = 20 GL 21 (1.45x103) x (0.5X153) XL = 4.56 n Xc = I - = WC 27&c 18.29 27 (1AS XIV ) (6x156) Xc= 54.66 = IR XR VR - Voltage in the resistor (VR) lox 12 sin (wt +0.2) VR = 120 sin (wt to.2) Voltage in capacitor (&) = 18.29x 12 sin (Wt 10.2) Vc = 219.48 sin (wt +0.2) VL Voltage in inductor (VLJ= ILXRL v= 4.56 x 12 sin (W++0.2) S4.72 xin (wt +0:2) Emsl= SuŘt (u - vet? Emfl = √ (20)2 + (54.72 - 18.29)' © Emsla

Emf= 14400+ (54.72 - 219.46) 2 Emf= 14400 + 27 145.85 | 12145.8 {mf = {mg = 112.89 Emd í 113 volt