electrical circuits hw7

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name: Mohammad Alhilal

institution: UTC

Homework 7 (Second Order Circuits) 1. Refer to the circuit shown below. find: (a) vR(0+) and vL(0+), (b) dvR(0+)/dt and dvL(0+)/dt, (c) vR(∞) and vL(∞). 2. The differential equation that describes the current in an RLC network is Given that i(0) = 0, di(0)/dt = 6 mA/s, obtain i(t). 3. If R = 50 Ω, L = 1.5 H, what value of C will make an RLC series circuit: (a) overdamped, (b) critically damped, (c) underdamped? 4. The switch in the circuit below moves from position A to position B at t = 0 (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Let v(0) = 0, find v(t) for t > 0 5. The switch in figure below moves from position A to position B at t = 0 (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Determine i(t) for t > 0. 6. A series RLC circuit is described by Find the response when L = 0.5 H, R = 4 Ω, and C = 0.2 F. Let i(0) = 1, di(0)/dt = 0. 7. For the circuit below, find v(t) for t >0. 8. Find the output voltage vo(t) in the circuit below. 9. For the circuit shown below, find i(t) for t > 0. 10. For the circuit below, find v(t) for t > 0. Assume that i(0+) = 2 A.

Tutor Answer

MercyJ54
School: Duke University

Attached.

Running head: Second Order Circuits

Electrical Circuits hw7
Mohammad Alhilal
UTC

Second Order Circuits
1. Refer to the circuit shown below. Find:

Solutions

Second Order Circuits

Second Order Circuits
2. The differential equation that describes the current in an RLC network
Solution
We know that
L (dn x/dx)
=sn . l(x) – sn-1 x(0) – sn-2 x1 (0) …….
Given RLC equations
(d2v/ dt2 ) + s. (dv/dt) + 4v = 0
Taking Laplace transform of RLC equation
S2V (S) – S V(0) – dv(0)/dt + 5S v(s) – v(0) - 4V (s) = 0
From given values
V(0) =0 , dv(0)/dt =5
S2 V(s) – s. (0) – 5 5 + 5SV(s) – 0 + 4 v(s) = 0
V9s0 = ( 5/ S2 + 5S +) = (5/S2 + 4S +S + 4) = (5/S(S+4) ...

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Anonymous
Thanks, good work

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