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Exam 3 - Circuit Resonance

For full credit all calculations and formulas must be shown. All numeric answers should be enclosed in a box or underlined twice. The exam will review course material relating to; frequency plots, bandwidth, AC sources, center frequency and -3dB bandwidth roll-off, Q point, inductive reactance, resonance, impedance plots, series resonant circuits, power and half power, amplitude and phase, and a circuits total impedance.

1. For the given circuit and frequency plot shown in Figure 1, determine the following:
a. Find the Bandwidth (BW)
b. Find the Resonance Frequency, Fr
c. Find Q
d. Find the Inductive Reactance at the Resonance Frequency
e. Find the value of the Inductive Coil, L
f. Find the value of the Capacitor, C
g. Find the value of the Voltage across the capacitor at resonance, VC
h. Find the Current at the center frequency, I at FC

2. Given the impedance plot in Figure 2 perform the following:
a. Draw a series resonant circuit that would product the plot in Figure 2.
b. What is the bandwidth of the circuit?
c. What is the Q of the circuit?
d. Is this a high Q or a low Q?

3. A Series Resonance circuit has a source voltage of 20 volts with a phase angle of 35 degrees. At the lower half power frequency (99KHz), the current I = 20mA. At the upper half power frequency (101KHz), the current is I = 20mA. Determine the following:
a. Find the resistance, R
b. Find the inductance, L
c. Find the capacitance, C
d. Find the resonance voltage and phase, Vr
e. Find the voltage across the capacitor and phase, VC
f. Find the voltage across the inductor and phase, VL

4. It is desired that the total impedance ZT of the circuit in Figure 3 be a resistor of 50K ohms at resonance. Calculate the following parameters:
a. Find the value of the inductive reactance, XL
b. Compute XC
c. Find the resonant frequency if the coil inductance is L = 16mH
d. Find the value of the capacitor, C

5. For the circuit in Figure 4
a. Find the value of XC at resonance
b. Find the total impedance, ZT at resonance
c. Find the currents flowing through the inductor IL, and the current through the capacitor IC
d. If the resonant frequency is 20KHz, find the values of L and C
e. Find QP and the bandwidth BW

Solutions: Provided in the Exam Notes Calculations Section below.

Solution Notes and Graphics:

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Engineering key words: Bandwidth, AC circuits, electronics test, examination, answers, solutions guide, quiescent point, capacitance, inductance, resistance, materials, impedance, resonance, cutoff, coils, specifications, phase, power, watts, milliamps, resonance freq, center freq, decibel, compression point, decade, log, dB, graphical plot, Q factor, voltage source, current source.

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