0195136047.pdf

114 TIME-DEPENDENT CIRCUIT ANALYSIS = (√ 2 Irmscosωt ) L ( − √ 2 ωIrmssinωt ) =−Irms^2 XLsin 2ωt (3.1.40) whereXL=ωLis the induc ...

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 115 EXAMPLE 3.1.5 Consider anRLCseries circuit excited byv(t)= ( 100 √ 2 cos 10t ) V ...

116 TIME-DEPENDENT CIRCUIT ANALYSIS φ = 24.23° S = VRMSIRMS = 456 VA PR = 415.9 W = PS QS = 187.1 VAR (d) QC = −20.8 VAR P^2 + Q ...

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 117 φ ωC 1 VR = R I VR + VL + VC = V VL + VC = j(ωL − ) I I = I ∠ 0 ° (Reference) (b ...

118 TIME-DEPENDENT CIRCUIT ANALYSIS − + + − + − V 1 = 462 ∠0 ̊ V I 1 VL =? P 1 = 5 kW Q 1 = kVAR G 1 − + G 2 S 1 = kVA P 2 =? Q ...

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 119 EXAMPLE 3.1.8 (a) Find the Thévenin equivalent of the circuit shown in Figure E3 ...

120 TIME-DEPENDENT CIRCUIT ANALYSIS (a) Since the Thévenin impedance is the ratio of the open-circuit voltage to the short-circu ...

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 121 Solution − + V (a) Inductive load Capacitor added (in parallel) for power factor ...

122 TIME-DEPENDENT CIRCUIT ANALYSIS whereω= 2 πf= 2 π/Tis thefundamentalangular frequency,a 0 is theaverageordinate or the dccom ...

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 123 (a) v(t) Vm t T Period T == 4 T 2 3T 4 2 π ω 1 f − + − + V VC 20 Ω = (c) − − ...

124 TIME-DEPENDENT CIRCUIT ANALYSIS I ̄= V ̄ 20 +( 10 /j ω) V ̄C= ( 10 jω ) I ̄= V ̄ 1 + 2 jω Treating each Fourier-series term ...

3.2 TRANSIENTS IN CIRCUITS 125 3.2 Transients in Circuits Thetotal responseof a system to an excitation that is suddenly applied ...

126 TIME-DEPENDENT CIRCUIT ANALYSIS however, that the functionestused here in finding transient solutions is not the generalized ...

3.2 TRANSIENTS IN CIRCUITS 127 Since we know that the inductor current cannot change its value instantaneously, as otherwise the ...

128 TIME-DEPENDENT CIRCUIT ANALYSIS 05 20 e−^1 = 7.36 20 e−^2 t/5 vL(t), V t, s T = 2.5^10 (b) 20 15 Figure E3.2.1Continued Aft ...

3.2 TRANSIENTS IN CIRCUITS 129 i(t) iR iC S I = 10 A vC(t) t = 0 R = 2 Ω C^ = 5 F − + (a) Figure E3.2.2(a)RC circuit excited by ...

130 TIME-DEPENDENT CIRCUIT ANALYSIS vC(t)andiC(t) are plotted in Figures E3.2.2(b) and (c). The following points are noteworthy. ...

3.2 TRANSIENTS IN CIRCUITS 131 (c) iL, ss(t) = −10/10 = −1 A 4 Ω S 5 Ω 6 Ω 10 V 5 A Short b a − + t = 0− vx(o−) + − − + (d) iL(o ...

132 TIME-DEPENDENT CIRCUIT ANALYSIS S t = 0 (a) iC(t) vC(t) 1 Ω 5 Ω vx(t) 10 V 4 Ω 5 F b + − a + − + − Figure E3.2.4 (b) Short 1 ...

3.2 TRANSIENTS IN CIRCUITS 133 In our example, vC(t)= ( − 40 9 + 10 ) e−t/^30 − 10 = ( 50 9 e−t/^30 − 10 ) V, fort> 0 In the ...