Explanation Given data: Refer to Figure 16.71 in the textbook. Formula used: Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (1) 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 (2) 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 (3) Here, C is the value of capacitance. Calculation: The given circuit is redrawn as shown in Figure 1. Apply Laplace transform for v s ( t ) to find V s ( s ) . V s ( s ) = 7.5 s + 2 { ∵ L ( e − a t u ( t ) ) = 1 s + a } Substitute 10 Ω for R in equation (1) to find Z R . Z R = 10 Substitute 0.25 H for L in equation (2) to find Z L . Z L = s ( 0.25 H ) = 0.25 s Substitute 0.2 F for C in equation (3) to find Z C . Z C = 1 s ( 0.2 F ) = 5 s Convert the Figure 1 into s -domain. Apply nodal analysis at node V o ( s ) for the circuit shown in Figure 2. V o ( s ) − 3 V x ( s ) 0.25 s + V o ( s ) ( 5 s ) + ( V o ( s ) − 7.5 s + 2 ) 10 = 0 V o ( s ) 0.25 s − 3 V x ( s ) 0.25 s + s V o ( s ) 5 + V o ( s ) 10 − 7.5 10 ( s + 2 ) = 0 V o ( s ) 0.25 s + s V o ( s ) 5 + V o ( s ) 10 − 7.5 10 ( s + 2 ) − 3 V x ( s ) 0.25 s = 0 V o ( s ) [ 1 0.25 s + s 5 + 1 10 ] − 7.5 10 ( s + 2 ) − 3 V x ( s ) 0.25 s = 0 Simplify the above equation as follows: V o ( s ) [ 1 0.25 s + s 5 + 1 10 ] − 7.5 10 ( s + 2 ) − 3 V x ( s ) 0.25 s = 0 V o ( s ) [ 40 + 2 s 2 + s ] − 7

EE 98: Fundamentals of Electrical Circuits - With Connect Access

6th Edition

ISBN: 9781259981807

Author: Alexander

Publisher: MCG

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Chapter 16, Problem 48P

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Find the expression of voltage across the resistor Vx(s) in the circuit of Figure 16.71.

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Chapter 16, Problem 47P

Chapter 16, Problem 49P

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For the circuit shown, let V₁ = 12 V, Is1 = 2A, Is2 = 4A, R₁ = 2, R2 = 4, and R3 = 6. Determine the current Io using Mesh method as follows: 1. Choose all meshes that must be included, if any, to construct the supermesh. 11, 13 O 11, 12 O 12, 13, 11 12, 13 O none of the above 2. Consider mesh (loop) iz, write the corresponding expression in terms of mesh currents i₁, 12, 13 as of the form (R11 · i₁ + R₁2 · 2 + R₁3-13 = V₁), then enter the corresponding values: R11 R12 R13 Ω Ω Ω V V₁₂ 3. Solve the above equation to determine then lo : 10 = Ist A R₁ ww ww R₂ + V₁ 1, R3 The relative tolerance for this problem is 7%. ww IS2

Enter the matrix values (numerical) to solve for mesh-currents i₁, iz and 13, for the circuit shown, using Mesh method. In the matrix, row 1, row 2, and row 3 correspond to i₁, 12 and 13, current expressions, respectively. Let Vs=15, R₁ =50, R₂-32, R3-8, R4-17, R5-29, and R=41. [R11 R12 R13 The matrix values are shown here: R21 R22 R23 = V₂ R31 R32 R33 [V3] The relative tolerance for this problem is 5%. R1 Loop i₁ R11 + Vs Ω R12 Ω R13 Ω V V₁= Loop 12 R21 Ω R22 Ω R23 Ω V V₂ Loop 13 Ω R31 R32 Ω R33 Ω V3= V R2 R4 R3 R5 R6

For circuit shown, use Mesh method to find the voltage Vo as follows. Enter, in the matrix format, as below, the loop currents, where row 1, and row 2, correspond to i₁, and i2 loop current expressions, respectively. Let Vs1-5, Vs2-15, R₁=5, R₂=2, and R3=8. The matrix values are shown here: [R11 R12 21 R21 R22 Rx - M - M iz = The relative tolerance for this problem is 5%. Vst (+- R1 ww Loop i₁ R115 G12 V₁ = Loop 12 R21 R22 V₂= Ω C C Ω V Ω 02 C V R₂ ww VS2 + Ry ww + Vo Use Cramer's rule (matrix), substitution, or any other method to calculate the voltages:

Chapter 16 Solutions

EE 98: Fundamentals of Electrical Circuits - With Connect Access

Ch. 16.2 - Determine vo(t) in the circuit of Fig. 16.6,...Ch. 16.2 - Prob. 2PP Ch. 16.2 - Prob. 3PP Ch. 16.3 - For the circuit shown in Fig. 16.12 with the same...Ch. 16.3 - Prob. 5PP Ch. 16.3 - The initial energy in the circuit of Fig. 16.17 is...Ch. 16.4 - Prob. 7PP Ch. 16.4 - Prob. 8PP Ch. 16.4 - Prob. 9PP Ch. 16.5 - Obtain the state variable model for the circuit...

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Find the expression of voltage across the resistor V x ( s ) in the circuit of Figure 16.71.

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Find the expression of voltage across the resistor Vx(s) in the circuit of Figure 16.71.

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