150V t=0 iR ic + 5 mH 200 n3 vc(t) 20 nF7 Fig.Q2 The switch in the circuit of Fig.Q2 has been opened for a long time and is closed at 1= 0. Analyse the circuit to find

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300 N
150V
t=0
i
iR
ic
5 mH
200 N3
20 nF Vc(t)
Fig.Q2
The switch in the circuit of Fig.Q2 has been opened for a long time and is closed at t 0.
Analyse the circuit to find
i)
ii)
the voltage across the capacitor, ve(t) for t2 0.
the current flowing through the inductor iL(t) for t20.
Appendix for Question 2
Damping
Natural Response Equations
Coefficient Equations
Overdamped
x(1) - Aje + Aze
x(0) - A, + Azi
dx/dr(0) - Ajs, + Asz
Underdamped
x(1) - (B, cos wt + B, sin a e
x(0) - B:
dx/dt(0) - -aB + waB2.
where w,- Va - a
Critically damped
x(1) - (D + D)e
x(0) - Dz.
dx/dr(0)
D- a D
Damping
Step Response Equations
Coefficient Equations
Overdamped
x(1) = X, + Aj e + Ase
x(0) = X, + Aj + A:
dx/dt(0) = Aj s1 + As s2
Underdamped
x(t) = X, + (Bị cos aat + B sin eaf et
x(0) = X, + Bị :
dx/dt(0) = -aB + aB
Critically damped
x(1) = X + Di tet + Det
x(0) = X, + D:
dx/dt(0) = D - «D
where X, is the final value of x(t).
Transcribed Image Text:300 N 150V t=0 i iR ic 5 mH 200 N3 20 nF Vc(t) Fig.Q2 The switch in the circuit of Fig.Q2 has been opened for a long time and is closed at t 0. Analyse the circuit to find i) ii) the voltage across the capacitor, ve(t) for t2 0. the current flowing through the inductor iL(t) for t20. Appendix for Question 2 Damping Natural Response Equations Coefficient Equations Overdamped x(1) - Aje + Aze x(0) - A, + Azi dx/dr(0) - Ajs, + Asz Underdamped x(1) - (B, cos wt + B, sin a e x(0) - B: dx/dt(0) - -aB + waB2. where w,- Va - a Critically damped x(1) - (D + D)e x(0) - Dz. dx/dr(0) D- a D Damping Step Response Equations Coefficient Equations Overdamped x(1) = X, + Aj e + Ase x(0) = X, + Aj + A: dx/dt(0) = Aj s1 + As s2 Underdamped x(t) = X, + (Bị cos aat + B sin eaf et x(0) = X, + Bị : dx/dt(0) = -aB + aB Critically damped x(1) = X + Di tet + Det x(0) = X, + D: dx/dt(0) = D - «D where X, is the final value of x(t).
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