ECE141_2009FALL_EXAM4__[0]

# ECE141_2009FALL_EXAM4__[0] - Department of Electrical...

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Unformatted text preview: Department of Electrical Engineering The Cooper Union ECE 141 Final Examination Circuits and Electronics I Fall 2009 1. The sources in the linear circuit given below are deﬁned by i,(t) = 10cos(4t) A, vs(t) == 2vL(t) mmvm=1mmmr+us)v 50011111 i(t) SW 49 to) 0 9 (t) M v(t) 3) Obtain the (b—domain model for the circuit. is) Write the (la-domain node voltage equations for the circuit. c) Write the ¢-domain mesh current equations for the circuit. (1) Determine the steady-state expression for the current i(t). 2. Steady—state is established in the linear circuit shown in the ﬁgure below with the switch closed. At t = 0, the switch is opened. The controlled source is defined by is = 0.4;. The uldependent sources are VI = 9V and V; = 18.5V. 69 7 unit t—O so 3) Determine i(0-) and v(O—) from the circuit at t = 0—. b) Determine i(0+) and v(0+) from the circuit at t = 0+. c) Determine i(°o) and v(oo) from the circuit as t » 0°. (1) Determine the expression for the current i(t). e) Determine the expression for the voltage v(t). 1) Give appropriately labeled sketches for the cunent Kit) and the voltage v(t). g) Determine the "expressions for the for the powers plft) and pz(t) associated with the voltage somces V, and V2, respectively. ECE 141 Final Examination Circuits and Electronics I Fall 2009 3 . Assume that the current source 1(t) in the RLC-circuit given below is sinusoidal of the form x(t) = chosmt + 6) A and that the circuit is operating under steady—state condition. + L i ii them) no 0' C no (output) 3) Obtain the (Ii-domain mode for the circuit. b) Use the (bwdomain modellliie ermine the appropriate input—output model G000) for the circuit deﬁned by Y := GUw)X where Y = P{y(t)} and X = P{x(t)]. Express the function Gﬁw) in the form 60w) = G(co)£G(jtu) where 6(a)) = lGGm)|. c) Determine the appropriate expression for the output y(t) due to the given form of the input x(t) and the input-output model Gﬁm). «1) Determine the expressions for the (Ii—domain input-output model Gate) and the Output y(t) if the frequency of the input x(t) is set equal to to = lit/LC. 4. The switch in the circuit shown below has been closed for along time before it is opened at t = 0. The sources are deﬁned by v5 = lDi(t), vA = 20V and i3 = 75A. Determine the validity or otherwise of each of the following statement: a) The circuit is nonlinear and time-invariant. b) The circuit is dynamic. c) The initial states of the circuit I0 and V" are given by L, = v0.5A and V0 = 15V. (1) This is a third-order circuit. e) The circuit is critically damped. l) The dependent source vs(t) as t a no is given by vim) = 12.5V. g) The energy trapped in the capacitors as t .. co is 1.8751. ECE 141 Final Examination Circuits and Electronics I . Fall 2009 5. The independent sources in the linear RLC-circuit shown in the ﬁgure below are deﬁned by v56) = 11V and £0) = lOcos(400t) A. The controlled source is deﬁned by i, = 2Vx. i(t] 30mH 12!} 25mH ‘l| . 1‘. a) Determine the steady-state expression for the voltage v(t). b) Determine the steady-state expression for the current i(t). ...
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