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Homework 1 - AC RLC Response and Phasors

Problem 12.
Determine the sinusoidal expression for the current, provided a 0.2H coil with the following voltages across the coil; (a) 1.5 sin(60t), (b) 0.016 sin(t + 4deg), (c) -4.8 sin(0.05t + 50deg), and (d) 9x10-3cos(377t + 360deg).
{ Solution }

Problem 14.
Determine the capacitance in microfarads if a capacitor has a reactance of (a) 250 ohms at 60Hz, (b) 55 ohms at 312Hz, and (c) 10 ohms at 25Hz.
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Problem 25.
The reactance of a coil equals the resistance of a 10K ohm resistor at a frequency of 5KHz. Determine the inductance of the coil.
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Problem 16.
The voltage across a 2.5ohm capacitive reactance is given below. Determine the sinusoidal expression for the current and sketch the voltage and current sinusoidal waveforms on the same axis.
a) 100 sin( wt )
b) 0.4 sin( wt + 20deg)
c) 8 cos( wt + 10deg)
d) -70 sin( wt + 40deg)
{ Solution }

Problem 19.
The current through a 0.5uF capacitor is provided below. Determine what the sinusoidal expression is for the voltage.
a) 0.20 sin(300t)
b) 0.007 sin(377t)
c) 0.048 cos(754t)
d) 0.08 sin(1600t - 80deg)
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Problem 23.
Basic RLC elements have predictable frequency responses. For this problem, plot Xc versus frequency for a 1uF capacitor using a frequency range of zero to 10KHz on a linear scale.
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Problem 26.
Determine the frequency at which a 1uF capacitor and a 10mH inductor will have the same reactance.
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Problem 46.
Provided the following complex number expressions, perform mathematical operations for each expression and express your answers in rectangular form:
a) [(4 + j3) + (6 - j8) / (3 + j3) - (2 + j3)]
b) [(8 angle 60deg) / (2 angle 0deg) + (100 + j100)]
c) [(6 angle 20deg)(120 angle -40deg)(3 + j4) / (2 angle - 30deg)
d) [(0.4 angle 60deg)2(300 angle 40deg) / (3 + j9)]
e) [(1 / (0.02 angle 10deg)2)(2/1j)3(1 / (62 - j(900)1/2))]
{ Solution }

Problem 48.
For each of the following expressions, express each in phasor form:
a) 21/2(100) sin( wt + 30deg)
b) 21/2(0.25) sin( 157t - 40deg)
c) 100 sin( wt - 90deg)
d) 42 sin( 377t + 0deg)
e) 6E-6 cos( wt )
f) 3.6E-6 cos( 754t - 20deg)
{ Solution }

Problem 53.
For the circuit diagram in Figure 1 below, find the sinusoidal expression for the input current from the source for the system provided:
I1 = 6E-3 sin(377t + 180deg)
I2 = 8E-3 sin(377t)
I3 = 2I2
{ Solution }





Homework Solutions and Calculations

Sinusoidal Current Expression
Capacitance Coil Inductance
Sinusoidal Waveforms
Capacitor Voltage Expression
RLC Frequency Reactance
Rectangular Phasor Calculations
Sinusoidal Input Source


Engineering key words: phasor form, rectangular form, circuit expression, angle, imaginary component, RLC, capacitance, inductance, resistance, reactance, frequency, sinusoidal waveform, current, voltage, AC signal, coil, response.


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