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ECE 307 – Exam 1
Fall 2003
Name (print):
September 26, 2003
This test is closed book and closed notes. You may use the single equation sheet you have hopefully brought to class. SHOW ALL WORK. Partial credit may be given.
1 Energy question (20 points)
Suppose that the voltage across two 1H inductors, in parallel, is the v(t) (shown below). Calculate the total current, i(t), through both inductors as a piecewise function of time, for all time. (−∞ < t < ∞).
v(t) =
0 , −∞ < t < 0 t^2 , 0 ≤ t < 2 0 , 2 ≤ t < ∞
i(t) =
HINT: Integration!
Calculate the total energy stored in both inductors combined, WTLeq , at t = 10.
Suppose that all the energy stored in both inductors combined at time t = 10 is some- how transfered to a single, initially uncharged, 1F capacitor. What would be the voltage, VC , across the capacitor after the transfer?
2 Charge and power question (20 points)
A 20 Volt light is rated at 1000 Watts.
2.1 Charge
What total charge flows through the light in 1 hour?
What is the cost of 10 days of operation at 10 dollars per kilowatt-hour?
4 Thevenin’s equiv (20 points)
Suppose there were a resistive load, RL attached between terminals b and c (in parallel with the 4 ohm resistor) in problem 3. Find the Thevenin’s equivalent of this circuit at nodes b, c as seen by the load, RL. Calculate the power, PRL , delivered to the load as a function of RL.
32 V
2 ohms a b
d
t = 0
C1 = 1F C2 = 1F
Figure 2: Schematic for problems 5 and 6
5 Initial and final conditions (20 points)
Suppose that the initial voltages across the capacitors, just before time t = 0 is VC 1 (0−) = VC 2 (0−) = 12. Find the initial current through the 2 ohm resistor, IR(0+) = IC 1 (0+)+IC 2 (0+) and initial capacitor voltages, VC 1 (0+) and VC 2 (0+), just after time t = 0. Find the steady-state current, IR(∞), through the resistor, and the voltages, VC 1 (∞) and VC 2 (∞) across the capacitors. Find the transient step response current, iR(t) through the resistor, if you can, for 5 points extra credit.
