 # Problem 1. In the following circuit, the capacitor was not charged...

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Problem 1. In the following circuit, the capacitor was not charged before switching. Find vC(t) for t > 0. Note that the circuit can be reduced to basic RLC. 14 6 2 4 A 14 V 2 H 0.02 F t 0 C v ! 1 Problem 2. The switch is flipped open at t = 0 in the following circuit. Find io(t) for t > 0 by using Laplace transform. Algebra hint: get rid of denominators in equations early. 5 5 2 A 5 H 0.2 F o i t 0 2 Problem 3. The transfer function of a system is H(jω) = jω (1000+jω)(100+jω) . Identify its break points, and sketch the straight line phase Bode plot. Indicate the slope of each straight line piece. 3 Problem 4. Determine what kind of filter the following circuit is, and find its cutoff frequency (or frequencies). In the circuit, R1 = 1 kΩ, R2 = 2 kΩ, C1 = 10 µF, and C2 = 1 µF. R3 R1 ! C2 C1 R2 Vs Vo 4 Problem 5. Determine only the hybrid parameters h11 and h21 of the following network. 5 10 j6 -j2 j2 j4 V1 ! ! V2 5 Problem 6. Find the output signal vo(t) in the following circuit with the given periodic source. Consider the following trig-identities: sin α sin β = 1 2 [− cos(α + β) + cos(α − β)], cos α cos β = 1 2 [cos(α + β) + cos(α − β)], and sin α cos β = 1 2 [sin(α + β) + sin(α − β)]. t cos 0.5 t S S v t s 3S 3S 4 0

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