PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 311

P.3.11 Let the impedance of a given circuit be given by Z = 7. 0 5 + j9.7 Ω, and the peak

sinusoidal voltage across be Vm = 60 V. Verify the following:

a. Z = 12 ∠54° Ω

b. Im = 5 A

c. Veff = 42.42 V

d. Ieff = 3.535 A

e. S = PAP = 150 va

f. P = 88.1 W

g. Q = Preac = 121.2 var

h. p(t) = Vm ⋅ Im [cos(θ) sin(2ωt) − (1/2)sin(θ) sin(2ωt)], where cos(θ) = cos(54°) = 0.588

and sin(θ) = sin(54°) = 0.809

i. Evaluate the maximum and minimum of p(t) by solving the equation given

by

dp(t)

_____

dt

= 0

Check if the solutions occur at ωt = 27 rad or 117 rad

and if pmax = 238 W

and

pmin = −61.7 W

P.3.12 A resistor of 50 Ω and an inductor of L = 0.1 H are connected in series where the

applied voltage is sinusoidal with 110 VRMS, and frequency f = 60 Hz. Verify the

following:

a. v(t) = 156 sin(2π 60 t) V

b. Z = 50 + j37.7 Ω

c. Z = 62.5 ∠37° Ω

d. I = 2.5 ∠–37° A

e. i(t) = 2.5 sin(2π 60 t − 37°) A

f. IRMS = 1.76 A

g. |Z| = 62.5 Ω

P.3.13 A series RC circuit consisting of a resistor R = 10 KΩ and a capacitor C = 10 μF, w it h

an applied voltage given by sine wave of 10 V, with a frequency of 1 kHz. Verify the

following:

a. v(t) = 14.14 sin 6283t V

b. Z = 10,000 − j15,900 Ω

c. Z = 18,800 ∠−58° Ω

d. I = 0.752 ∠58° mA

e. i(t) = 0.752 sin(6283t + 58°) mA

f. IRMS = 0.532 mA

g. VR(peak) = 7.52 V

h. VR(RMS) = 5.32 V

i. VC(peak) = 11.96 V

j. VC(RMS) = 8.46 V