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N. Cotter |
PRACTICE FINAL EXAM |
1. (50 points)
After having been open for a long time, the switch is closed at t = 0.
R1 = 12.5Ω R2 = 12.5Ω L = 6.25 μH
a. Two capacitances are available: 2 nF and 250 nF. Specify the value of C that will make v(t) overdamped.
b. Using the value of C found in (a), write a time-domain expression for v(t).
2. (50 points)
a. Determine the coefficients of the Fourier series, an, an, and bn, for the periodic waveform vi(t). Also, use these Fourier coefficients to find the coefficients of the first five terms of the Fourier series written in terms of inverse phasors:
Note any symmetry properties of the waveform that you use to determine coefficients.
b. The circuit on the left is a filter with output vo(t). Design a circuit to be placed in the box such that the filter rejects the fundamental frequency of vi(t) and has a bandwidth of 10,000 rad/sec. Specify the component values. Show how the components are connected in the circuit.
3. (50 points)
The initial energy stored in the circuit is zero.
R2 = 500 Ω L = 200 mH
a. Choose values of R1 and C to accomplish the following:
(1) v(t) and i(t) are decaying sinusoids 90° out of phase with each other.
(2) 1/α = T, where α is the exponential decay constant and T is the period of oscillation of the decaying sinusoid.
b. With the component values you chose in the circuit, write numerical expressions for v(t) and i(t).
4. (50 points)
Z1 = (5 - j5)Ω Z2 = (20 + j20)Ω
a. Find the input impedance, zin = V1/I1, for the above circuit.
b. Using zin from (a), find a numerical expression for VAB in the circuit below.
Balanced three-phase system.
Van = 52 ∠ 0°V Vbn = 52 ∠ −120°A zline = j12 Ω