Test 2 - Spring 2005
1. Determine the reactive power (Q) and the average power (P)
delivered by the voltage source. Be sure to include units as appropriate.
2. What percentage of the reactive power in the circuit above
is converted into a non-electrical form?
3. In the circuit shown, the load is to consist of a resistor
in series with one other component, either a capacitor or an inductor.
If maximum power is to be transferred to the load, determine the
value of the resistance as well as what the other component is
and its value.
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4. Determine the Line current IaA
and the Line - to - Line voltage at the load VCA.
The voltage source values are rms values.
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5. If the load in problem 4 on the previous page was converted
to a delta configuration, what would be the impedance per phase?
Give your answer in rectangular form.
6. For the three phase circuit of problem 4 modified as in
problem 5 (an equivalent delta-connected load instead of a Wye
connected load, determine the phase current IAB.
7. Prove that the Laplace Transform of f(t)
= A u(t) is F(s) = A / s by evaluating the Laplace integral. Be
sure to clearly show ALL steps if you wish full credit.
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8. Write a single integro-differential equation
which describes the behavior of the circuit shown after the switch
closes at t = 0. You may assume the initial voltage across the
capacitor is zero. Your equation should contain only a single
voltage or current variable. Be SURE to clearly label the variable
you choose on the circuit diagram.
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9. Express the function f(t) shown in the graph
below using unit step functions.
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10. Find f(t) for the following function by performing
a partial fraction expansion followed by an inverse Laplace transform.
Note that your final answer will be expressed in terms of a and
b. You must show ALL of your work for credit on this problem.
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11. In a circuit containing a resistor R, a capacitor
C, an inductor L, and a 20 volt source, the current through the
capacitor has been described by the Laplace transform of an integro-differential
equation given by
Determine an expression for VC(s),
the Laplace transform of the voltage across the capacitor. You
may assume that the capacitor has no initial charge stored in
it.
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