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Unit 1 |
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N. Cotter |
PRACTICE EXAM |
1. (25 points)
vg is a dc voltage source
After having been open for a long time, the switch is closed at t = 0.
a. Give expressions for i1(0+) and i1´(0+), (i.e., di1/dt at t = 0+), in terms of no more than vg, Ro, R, L, and C.
b. For L = 10 μH, choose R and C so that the system is underdamped and
α = 3⋅106 rad/s, ωd = 4⋅106 rad/s.
2. (25 points)
At t = 0, vg(t) switches instantaneously from -vo to +vo.
a. Write the state-variable equations in terms of the state vector
b. Evaluate the state vector x at t = 0+.
3. (50 points)
a. After being closed for a long time, the switch is opened at t = 0. Write a numerical time-domain expression for i(t), the current through the capacitance. This expression must not contain any complex numbers.
b. State whether i(t) is underdamped, overdamped, or critically damped.