(a) Explanation Formula used: The expression for parallel combination of inductance is as follows. 1 L = ( 1 L 1 + 1 L 2 ) (1) Here, L is the total inductance and L 1 and L 2 are the inductances in the circuit. The expression for series combination of inductance is as follows. L = ( L 1 + L 2 ) (2) Here, L is the total inductance and L 1 and L 2 are the inductance s in the circuit. The expression for KCL at node A is as follows. v A R 1 − i 2 + v A R 2 + v A R 3 = 0 (3) Here, i 2 isthe current in the circuit, v A is the voltage at node A and R 1 , R 2 and R 3 are the resistances in the circuit. The expression for current is as follows. i = v R (4) Here, i is the current, v is the voltage and R is the resistance. The expression for series combination of resistance is as follows. R = ( R 1 + R 2 ) (5) Here, R is the total resistances and R 1 and R 2 are the resistances in the circuit. The expression for the circuit time constant is as follows. τ = L R (6) Here, τ is the circuit time constant, R is the equivalent resistance across the inductor and L is the value of inductance. The expression for the current through inductor is as follows. i ( t ) = i ( 0 ) e − t τ (7) Here, i ( t ) is the current flowing through inductor, i ( 0 ) is the current through inductor at t > 0 , t is the given time and τ is the circuit time constant. Calculation: The circuit diagram is redrawn as shown in Figure 1. Refer to the redrawn Figure 1. As L 2 and L 3 are in parallel therefore from equation (1). 1 L 4 = ( 1 L 2 + 1 L 3 ) 1 L 4 = 1 1 H + 1 2 H 1 L 4 = 1 2 3 H (8) Rearrange equation (8) for L 4 . L 4 = 2 3 H The circuit diagram is redrawn as shown in Figure 2. As L 1 and L 4 are in series therefore from equation (2), L = ( L 1 + L 4 ) = 3 H + 2 3 H = 11 3 H The circuit diagram is redrawn as shown in Figure 3 for t < 0 . Refer to the redrawn Figure 3. At t = 0 − the inductor in the R L circuit is connected for long time. So, inductor behaved as short circuit. Substitute 5 A for i 2 , 8 Ω for R 1 , 3 Ω for R 2 and 2 Ω for R 3 in the equation (3), v A 8 Ω − 5 A + v A 3 Ω + v A 2 Ω = 0 3 v A − 120 A+8 v A + 12 v A 24 Ω = 0 23 v A − 120 A 24 Ω = 0 (9) Rearrange equation (9) for v A

9th Edition

ISBN: 9780073545516

Author: Hayt, William H. (william Hart), Jr, Kemmerly, Jack E. (jack Ellsworth), Durbin, Steven M.

Publisher: Mcgraw-hill Education,

See similar textbooks

Concept explainers

Graph theory

It is that part of network analysis where the configuration is called graph or structure of the network system when all of the elements (e.g., R, L, and C) in a network system are substituted with lines having circles/rings or dots across both endpoints.…

Question

Chapter 8, Problem 29E

(a)

To determine

Obtain expression for current i1(t) and current iL(t).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8, Problem 28E

Chapter 8, Problem 30E

Students have asked these similar questions

NO AI. NEED EXPLANATION ALSO PLEASE

I need help with this problem and an step by step explanation of the solution from the image described below. (Introduction to Signals and Systems)

Chapter 8 Solutions

Engineering Circuit Analysis

Ch. 8.1 - For the circuit in Fig. 8.2, what value of...Ch. 8.1 - Noting carefully how the circuit changes once the...Ch. 8.2 - In a source-free series RC circuit, find the...Ch. 8.3 - Prob. 4P Ch. 8.3 - Prob. 5P Ch. 8.4 - Prob. 6P Ch. 8.4 - Prob. 7P Ch. 8.4 - Prob. 8P Ch. 8.5 - Evaluate each of the following at t = 0.8: (a)...Ch. 8.6 - For the circuit of Fig. 8.37, find vc(t) at t...

Ch. 8.7 - Prob. 11P Ch. 8.7 - The voltage source 60 40u(t) V is in series with...Ch. 8.7 - Prob. 13P Ch. 8.8 - Prob. 14P Ch. 8.8 - Prob. 15P Ch. 8 - A source-free RC circuit has R = 4 k and C = 22 F,...Ch. 8 - A source-free RC circuit has v(0) = 12 V and R =...Ch. 8 - The resistor in the circuit of Fig. 8.51 has been...Ch. 8 - Prob. 4E Ch. 8 - Prob. 5E Ch. 8 - Prob. 6E Ch. 8 - Prob. 7E Ch. 8 - Prob. 8E Ch. 8 - Prob. 9E Ch. 8 - The switch in Fig. 8.56 has been closed for a long...Ch. 8 - For the circuit in Fig. 8.56, find (a) the total...Ch. 8 - Design a capacitor-based circuit that can achieve...Ch. 8 - (a) Graph the function f (t) = 10e2t over the...Ch. 8 - The current i(t) flowing through a 1 k resistor is...Ch. 8 - Radiocarbon dating has a similar exponential time...Ch. 8 - For the circuit of Fig. 8.4, compute the time...Ch. 8 - Design a circuit which will produce a current of 1...Ch. 8 - Prob. 18E Ch. 8 - Prob. 19E Ch. 8 - Referring to the circuit shown in Fig. 8.11,...Ch. 8 - Prob. 21E Ch. 8 - With the assumption that the switch in the circuit...Ch. 8 - The switch in Fig. 8.57 has been closed since...Ch. 8 - The switch in the circuit of Fig. 8.58 has been...Ch. 8 - Assuming the switch initially has been open for a...Ch. 8 - (a) Obtain an expression for v(t), the voltage...Ch. 8 - For the circuit of Fig. 8.61, determine ix, iL,...Ch. 8 - Prob. 28E Ch. 8 - Prob. 29E Ch. 8 - Prob. 30E Ch. 8 - Prob. 31E Ch. 8 - (a) Obtain an expression for vx as labeled in the...Ch. 8 - Prob. 33E Ch. 8 - Prob. 34E Ch. 8 - Prob. 35E Ch. 8 - Prob. 36E Ch. 8 - Prob. 37E Ch. 8 - The switch in Fig. 8.70 is moved from A to B at t...Ch. 8 - Prob. 39E Ch. 8 - Prob. 40E Ch. 8 - Evaluate the following functions at t = 1, 0, and...Ch. 8 - Prob. 42E Ch. 8 - Prob. 43E Ch. 8 - Prob. 44E Ch. 8 - You can use MATLAB to represent the unit-step...Ch. 8 - With reference to the circuit depicted in Fig....Ch. 8 - For the circuit given in Fig. 8.75, (a) determine...Ch. 8 - Prob. 48E Ch. 8 - Prob. 49E Ch. 8 - You build a portable solar charging circuit...Ch. 8 - The switch in the circuit of Fig. 8.78 has been...Ch. 8 - The switch in the circuit of Fig. 8.78 has been...Ch. 8 - Prob. 53E Ch. 8 - Prob. 54E Ch. 8 - Prob. 55E Ch. 8 - For the circuit represented in Fig. 8.82, (a)...Ch. 8 - Prob. 58E Ch. 8 - Prob. 59E Ch. 8 - For the circuit given in Fig. 8.85, (a) determine...Ch. 8 - The circuit depicted in Fig. 8.86 contains two...Ch. 8 - Prob. 62E Ch. 8 - Prob. 63E Ch. 8 - A series RL circuit has a voltage that steps from...Ch. 8 - For the two-source circuit of Fig. 8.89, note that...Ch. 8 - (a) Obtain an expression for iL as labeled in Fig....Ch. 8 - Obtain an expression for i(t) as labeled in the...Ch. 8 - Obtain an expression for i1 as indicated in Fig....Ch. 8 - Plot the current i(t) in Fig. 8.93 if (a) R = 10 ;...Ch. 8 - A dc motor can be modeled as a series RL circuit...Ch. 8 - Prob. 71E Ch. 8 - Prob. 72E Ch. 8 - A series RC sequentially switched circuit has R =...Ch. 8 - Refer to the circuit of Fig. 8.95, which contains...Ch. 8 - In the circuit of Fig. 8.95, a 3 mF capacitor is...Ch. 8 - Prob. 78E

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.

Obtain expression for current i 1 ( t ) and current i L ( t ) .

Solution Summary: The author explains how to obtain expressions for current and series combination of inductance.

Concept explainers

Obtain expression for current i1(t) and current iL(t).

Want to see the full answer?

Chapter 8 Solutions