Homework 1 – Electric Circuits II
1. If −10cos ωt + 4 sin ωt = Acos(ωt + φ ) , where A>0 and −180° < φ < 180° , find A and φ.
R= A = 10.8, φ = 21.8°
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2. If 200cos(5t + 130°) = F cos5t + G sin5t , find F and G.
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R= F = −129,G = −153
3. Given the two sinusoidal waveforms, f (t) = −50cosωt − 30sin ωt and
g(t) = 55cos ωt −15sin ωt , find (a) the amplitude of each, and (b) the phase angle by
which f(t) leads g(t)
R= (a) Amplitude f(t)=58.3, g(t)=57.0 (b) 133.8°
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4. Evaluate and express the result in rectangular form:
a) [(2∠30°)(5∠ −110°)](1+ j2)
b) (5∠ − 200°) + 4∠20°
R= (a) 21.4 − j6.38 ; (b) −0.940 + j3.08
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5. Evaluate and express the result in polar form:
a) (2 − j7) /(3 − j)
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b) 8 − j4 + [(5∠80°) /(2∠20°)]
R= (a) 2.30∠ − 55.6° ; (b) 9.43∠ −11.22°
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6. Find the complex voltage that results when the complex current 4e j 800t A is
applied to the series combination of a 1‐mF capacitor and a 2‐Ω resistor.
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R= 9.43e j(800t−32.0°) V
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7. Find the complex current that results when the complex voltage 100e j 2000t V is
applied to the parallel combination of a 10‐mH inductor and a 50‐Ω resistor.
R= 5.39e j(2000t−68.2°) A
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8. Transform each of the following functions of time into phasor form:
a) −5sin(580t −110°)
b) 3cos(600t) − 5sin(600t + 110°)
c) 8cos(4t − 30°) + 4 sin(4t −100°)
R= (a) 5∠ − 20° ; (b) 2.41∠ −134.8° ; (c) 4.46∠ − 47.9°
9. Let ω = 2000 rad/s and t = 1 ms. Find the instantaneous value of each of the
€ currents given
€ here in phasor€form:
a) j10 A
b) 20 + j10 A
c) 20 + j(10∠20°) A
R= (a)‐9.09 A; (b)­17.42 A; (c)‐15.44 A
f.perez@correo.ler.uam.mx