Explanation Given data: Refer to given circuit in the textbook. The value of current ( i g ) is, i g = 5 u ( t ) mA (1) Formula used: Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (2) Here, R is the value of resistance. Write a general expression to calculate the impedance of an inductor in s -domain. Z L = s L (3) Here, L is the value of inductance. Write a general expression to calculate the impedance of a capacitor in s -domain. Z C = 1 s C (4) Here, C is the value of capacitance. Calculation: The given circuit is redrawn as shown in Figure 1. Apply Laplace transform for equation (1) to find I g . I g = 5 mA s { ∵ L ( u ( t ) ) = 1 s } = 5 × 10 − 3 s Substitute 200 Ω for R in equation (2) to find Z R . Z R = 200 Substitute 40 mH for L in equation (3) to find Z L . Z L = s ( 40 mH ) = s ( 40 × 10 − 3 ) { ∵ 1 m = 10 − 3 } = 0.04 s Substitute 250 nF for C in equation (4) to find Z C . Z C = 1 s ( 250 nF ) = 1 s ( 250 × 10 − 9 F ) { ∵ 1 n = 10 − 9 } = 4 × 10 6 s Now, the Figure 1 is reduced as shown in Figure 2. Refer to Figure 2, the voltage across the impedance of capacitor is V ϕ . Apply voltage division rule in Figure 2 to find V ϕ . V ϕ = ( 4 × 10 6 s 200 + 4 × 10 6 s ) V o = ( 4 × 10 6 s 200 s + 4 × 10 6 s ) V o = ( 4 × 10 6 200 s + 4 × 10 6 ) V o Apply Kirchhoff’s current law in Figure 2. − 5 × 10 − 3 s + V o 200 + 4 × 10 6 s + 3.75 × 10 − 3 V ϕ + V o 0.04 s = 0 − 5 × 10 − 3 s + V o 200 s + 4 × 10 6 s + 3.75 × 10 − 3 V ϕ + V o 0.04 s = 0 s V o 200 s + 4 × 10 6 + 3.75 × 10 − 3 V ϕ + V o 0.04 s = 5 × 10 − 3 s Substitute ( 4 × 10 6 200 s + 4 × 10 6 ) V o for V ϕ in above equation. s V o 200 s + 4 × 10 6 + 3.75 × 10 − 3 ( ( 4 × 10 6 200 s + 4 × 10 6 ) V o ) + V o 0.04 s = 5 × 10 − 3 s s V o 200 s + 4 × 10 6 + 15000 V o 200 s + 4 × 10 6 + V o 0.04 s = 5 × 10 − 3 s ( s + 15000 ) V o 200 s + 4 × 10 6 + 25 V o s = 5 × 10 − 3 s V o [ ( s + 15000 ) 200 s + 4 × 10 6 + 25 s ] = 5 × 10 − 3 s Simplify the above equation as follows: V o [ s ( s + 15000 ) + 25 ( 200 s + 4 × 10 6 ) s ( 200 s + 4 × 10 6 ) ] = 5 × 10 − 3 s V o [ s 2 + 15000 s + 5000 s + 10 8 s ( 200 s + 4 × 10 6 ) ] = 5 × 10 − 3 s V o [ s 2 + 20000 s + 10 8 200 s ( s + 20000 ) ] = 5 × 10 − 3 s Simplify the above equation to find V o

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

See similar textbooks

Concept explainers

Current Division Method

The generalized current divider formula is given by the following relation below,

Videos

Question

Chapter 13, Problem 26P

To determine

Find the time domain expression of vo for the given circuit.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13, Problem 25P

Chapter 13, Problem 27P

Students have asked these similar questions

Consider the circuit in Fig. 4. (a) Use mesh analysis to find the currents i1, i2, i3. Hint use the supermode method. (10 marks) (b) Determine the Thévenin equivalent of the circuit that is connected to the dependent source (10 marks). (c) If the dependent source was replaced with a load resistor, what would be the value of its resistance so that the load would receive the maximum power from the rest of the circuit? (2 mark)

Formal Charge Distribution vs Oxidation States Te- For the Lewis diagram, above, determine: 0 The overall charge of the molecular species shown. -2 The formal charge on the tellurium atom. +7 The formal oxidation number of the tellurium atom. 1 pts Submit Answer Incorrect. Tries 3/5 Previous Tries Review: • For overall charge, compare the number of electrons depicted with the sum of the valence electrons for the free atoms. (Remember that an electron has a negative charge.) • Rules Governing Formal Charge • Rules for Assigning Oxidation States.

. (a) Use mesh analysis to find the current i. (b) Determine the Norton equivalent of the circuit that is connected to the 5 ohm resistor (c) If the 5 ohm resistor was replaced with a load resistor, what would be the value of its resistance so that the load would receive the maximum power from the rest of the circuit?

Chapter 13 Solutions

Electric Circuits. (11th Edition)

Ch. 13.2 - The parallel circuit in Example 13.1 is placed in...Ch. 13.3 - Prob. 2AP 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) =...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Find the time domain expression of v o for the given circuit.

Concept explainers

Videos

Find the time domain expression of vo for the given circuit.

Want to see the full answer?

Chapter 13 Solutions