310 Practical MATLAB® Applications for Engineers
3.5 Application Problems
P.3.1 Which of the following relations hold
a. 3 ∠135° = −3 cos(ωt − 45°)
b. − 2 + j2 = −2.82 cos(ωt − 45°)
c. − 3 − j4 = −5 cos(ωt + 53°)
d. 3 ∠300° = 3 cos(ωt − 60°)
e. 4 ∠−225° = −4 cos(ωt − 45°)P.3.2 A sine wave x(t) has a frequency of f = 1000 Hz, a peak value of 3.0, and a phase
angle of −45°.
a. Determine its period T and angular frequency ω
b. Obtain the equation for x(t)
c. Sketch by hand x(t) versus degrees, radians, and time
d. Write a program that returns the plots for part c over two complete cycles
P.3.3 Verify that the current is 53.8 A with a phase Φ = 57°30’, when a 200 V RMS, 50 Hz
is applied to a series RL circuit with R = 2 Ω and L = 0.01 H.
P.3.4 Verify using MATLAB that 100 ∠ 45 + 80 ∠120° = 30.7 + j140.
P.3.5 Verify that if V = 100 ∠45° and Z = 20 ∠60°, then I = 5 ∠–15°, by hand and by using
MATLAB.
P.3.6 Verify that if V = 50 + j75 V and I = 3 + j5 A, then its power is 225 + j475 W.
P.3.7 Show that when the frequency is 151 Hz and its impedance is 28.8 ∠80° Ω, then the
current is lagging the voltage by 80° if the circuit is a series RL, with R = 5 Ω and
L = 30 mH.
P.3.8 Let the impedance of a given circuit be Z = 15 + 20j Ω, and the voltage across it be
v(t) = 100 cos(100t) V. Verify that the current through it is i(t) = 4 cos(100t − 53°8’) A.
P.3.9 For the problem P.3.8, verify that Z is equivalent to an inductor L = .2 H in series
with a resistor R = 15 Ω.
P.3.10 For what frequency is the series RLC circuit of Figure 3.88 equivalent to the parallel
RC circuit of Figure 3.89?
R = 20 Ω L = 0.02 H C = 20 μFFIGURE 3.88
Series network diagram of P.3.10.
R = 20 Ω C = 23.1 μFFIGURE 3.89
Parallel network diagram of P.3.10.