a. Find the total number of watts, volt-amperes reactive, volt-amperes, and power factor FP for the network in Fig. 20.23. b. Sketch a load diagram and power triangle. c. Find the energy dissipated by the resistor over one full cycle of the input voltage if the frequency of the input quantities is

Question

a. Find the total number of watts, volt-amperes reactive, volt-amperes, and power factor [latex]F_P[/latex] for the network in Fig. 20.23.

b. Sketch a load diagram and power triangle.

c. Find the energy dissipated by the resistor over one full cycle of the input voltage if the frequency of the input quantities is 60 Hz.

d. Find the energy stored in, or returned by, the capacitor or inductor over one half-cycle of the power curve for each if the frequency of the input quantities is 60 Hz.

Accepted Answer

a. [latex]I=\frac{E}{Z_T}=\frac{100 V ∠0°}{6 Ω + j 7 Ω - j 15 Ω}=\frac{100 V ∠0°}{10 Ω ∠-53.13°}=10 A ∠53.13°\[0.5cm] V_R=(10 A ∠53.13°)(6 Ω ∠0°) = 60 V ∠53.13°\[0.5cm] V_L=(10 A ∠53.13°)(7 Ω ∠90°) = 70 V ∠143.13°\[0.5cm] V_C=(10 A ∠53.13°)(15 Ω ∠-90°) = 150 V ∠-36.87°\[0.5cm] P_T=EI cos \theta = (100 V)(10 A) cos 53.13° = 600 W \[0.5cm] =I^2R=(10A)^2(6\Omega)=600W\[0.5cm] =\frac{V^{2}_{R}}{R}=\frac{(60V)^2}{6}=600W\[0.5cm] S_T=EI = (100 V)(10 A) = 1000 VA\[0.5cm] =I^2Z_T=(10A)^2(10 Ω) = 1000 VA \[0.5cm] =\frac{E^2}{Z_T}=\frac{(100V)^2}{10 Ω}=1000VA\[0.5cm] Q_T = EI sin \theta = (100 V)(10 A) sin 53.13° = 800 VAR\[0.5cm] =Q_C - Q_L\[0.5cm] =I^2(X_C - X_L) = (10 A)^2(15 Ω - 7 Ω) = 800 VAR\[0.5cm] Q_T=\frac{V^{2}_{C}}{X_C}-\frac{V^{2}_{L}}{X_L}=\frac{(150V)^2}{15 Ω}-\frac{(70V)^2}{7 Ω}=1500 VAR(C) - 700 VAR(L) = 800 VAR (C)\[0.5cm] F_p=\frac{P_T}{S_T}=\frac{600 W}{1000VA}=0.6\; leading(C) [/latex]

b. The load diagram is as shown in Fig. 20.24(a) and the power triangle in Fig. 20.24(b).

c. [latex]W_R=\frac{V_RI}{f_1}=\frac{(60 V)(10 A)}{60 Hz}=10j [/latex]

d. [latex]W_L=\frac{V_LI}{\omega_1}=\frac{(70 V)(10 A)}{(2\pi)(60 Hz)}=\frac{700 J}{377}=1.86 J\[0.5cm] W_C=\frac{V_CI}{\omega_1}=\frac{(150 V)(10 A)}{377 rad/s}=\frac{1500 J}{377}=3.98 J [/latex]

Question 20.4: a. Find the total number of watts, volt-amperes reactive, vo...

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