(a) Explanation Given data: Refer to given circuit in the textbook. The expression of voltage is, v ( t ) = ρ R e − R L e t u ( t ) V (1) The expression of current i 1 ( t ) is, i 1 ( t ) = ρ L 1 + L 2 [ L 1 + L 2 e ( − R L e ) t ] u ( t ) A (2) The expression of current i 2 ( t ) is, i 2 ( t ) = ρ L 1 L 1 + L 2 [ 1 − e ( − R L e ) t ] u ( t ) A (3) Calculation: Substitute ∞ for R in equation (1) to find v ( t ) . v ( t ) = ρ ( ∞ ) e − ∞ L e t u ( t ) V = ∞ Since the value of voltage is tends to infinity calculate the area under the impulse function to find v ( t ) . Area = ∫ 0 t ρ R e − R L e t u ( t ) V = ρ R [ e − R L e t ( − R L e ) ] 0 t = ρ L e [ − e − R L e t ] 0 t = ρ L e [ − e − R L e t + e − R L e ( 0 ) ] = ρ L e [ 1 − e − R L e t ] { ∵ e 0 = 1 } Substitute ∞ for R in above equation to find v ( t ) under impulse function. Area = ρ L e [ 1 − e − ∞ L e t ] = ρ L e [ 1 − 0 ] { ∵ e − ∞ = 0 } = ρ L e Therefore, v ( t ) → ρ L e δ ( t ) since the area under the impulse function is ρ L e (b) To determine Find the time domain expressions of v ( t ) , i 1 ( t ) and i 2 ( t ) for R = ∞ .

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ISBN: 9780133760033

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Question

Chapter 13, Problem 85P

(a)

To determine

Find the time domain expressions of v(t), i1(t) and i2(t) for R→∞.

(b)

To determine

Find the time domain expressions of v(t), i1(t) and i2(t) for R=∞.

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Chapter 13, Problem 84P

Chapter 13, Problem 86P

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Chapter 13 Solutions

Electric Circuits (10th Edition)

Ch. 13.2 - Prob. 1AP Ch. 13.2 - The parallel circuit in Example 13.1 is placed in...Ch. 13.3 - Prob. 3AP Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.3 - The dc current and dc voltage sources are applied...Ch. 13.3 - Prob. 6AP Ch. 13.3 - Using the results from Example 13.7 for the...Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.4 - Derive the numerical expression for the transfer...Ch. 13.5 - Find (a) the unit step and (b) the unit impulse...

Ch. 13.5 - The unit impulse response of a circuit is υo(t) =...Ch. 13.7 - The current source in the circuit shown is...Ch. 13.7 - For the circuit shown, find the steady-state...Ch. 13 - Prob. 1P Ch. 13 - Prob. 2P Ch. 13 - Prob. 3P Ch. 13 - Prob. 4P Ch. 13 - An 8 kΩ resistor, a 25 mH inductor, and a 62.5 pF...Ch. 13 - Prob. 6P Ch. 13 - Find the poles and zeros of the impedance seen...Ch. 13 - Find the poles and zeros of the impedance seen...Ch. 13 - Prob. 9P Ch. 13 - Prob. 10P Ch. 13 - Prob. 13P Ch. 13 - Prob. 15P Ch. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - Prob. 25P Ch. 13 - Prob. 28P Ch. 13 - The switch in the circuit seen in Fig. P13.32 has...Ch. 13 - Prob. 31P Ch. 13 - Prob. 33P Ch. 13 - Prob. 35P Ch. 13 - Prob. 46P Ch. 13 - Prob. 47P Ch. 13 - Find the transfer function H(s) − Vo/Vi for the...Ch. 13 - Prob. 49P Ch. 13 - Prob. 50P Ch. 13 - Prob. 51P Ch. 13 - Prob. 53P Ch. 13 - Prob. 54P Ch. 13 - The operational amplifier in the circuit in Fig....Ch. 13 - Find the transfer function Io/Ig as a function of...Ch. 13 - Prob. 58P Ch. 13 - Prob. 59P Ch. 13 - Prob. 60P Ch. 13 - Prob. 61P Ch. 13 - Assume the voltage impulse response of a circuit...Ch. 13 - Prob. 68P Ch. 13 - The input voltage in the circuit seen in Fig....Ch. 13 - Find the impulse response of the circuit shown in...Ch. 13 - Prob. 73P Ch. 13 - Prob. 74P Ch. 13 - Prob. 75P Ch. 13 - The op amp in the circuit seen in Fig. P13.81 is...Ch. 13 - Prob. 78P Ch. 13 - The transfer function for a linear time-invariant...Ch. 13 - Prob. 80P Ch. 13 - Prob. 81P Ch. 13 - Prob. 82P Ch. 13 - Prob. 84P Ch. 13 - Prob. 85P Ch. 13 - The parallel combination of R2 and C2 in the...Ch. 13 - Show that if R1C1 = R2C2 in the circuit shown in...Ch. 13 - The switch in the circuit in Fig P13.91 has been...Ch. 13 - Prob. 90P Ch. 13 - Prob. 91P

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