Explanation Given data: Refer to Figure 16.62 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. For a DC circuit, at steady state condition at time t = 0 − the capacitor acts like open circuit and the inductor acts like short circuit Now, the Figure 1 is reduced as shown in Figure 2. Refer to Figure 2, the voltage across the capacitor is same as the source voltage ( v s ) Since the capacitor is open circuited, there is no current flows through the inductor. v C ( 0 − ) = 20 V i L ( 0 − ) = 0 A The current through inductor and voltage across capacitor is always continuous so that, i ( 0 ) = i L ( 0 − ) = i L ( 0 + ) = 0 A v ( 0 ) = v C ( 0 − ) = v C ( 0 + ) = 20 V For time t > 0 , the circuit remains same as shown in Figure 1. Substitute 1 Ω for R 1 in equation (1) to find Z R 1 . Z R 1 = 1 Substitute 3 Ω for R 2 in equation (1) to find Z R 2 . Z R 2 = 3 Substitute 1 H for L in equation (2) to find Z L . Z L = s ( 1 H ) = s Substitute 1 F for C in equation (3) to find Z C . Z C = 1 s ( 1 F ) = 1 s Apply Laplace transform for i s ( t ) to find I s ( s ) . I s ( s ) = 40 s { ∵ L ( u ( t ) ) = 1 s } The voltage source is written as follows: v s = 20 ( 1 ) V = 20 u ( t ) V { ∵ u ( t ) = 1 for t > 0 } Apply Laplace transform for above equation to find V s ( s ) . V s ( s ) = 20 s { ∵ L ( u ( t ) ) = 1 s } Using element transformation methods with initial conditions convert the Figure 1into s -domain. Apply Kirchhoff’s voltage law for the circuit shown in Figure 3. ( 1 ) I ( s ) − 40 s + 3 I ( s ) + s I ( s ) + 20 s − v ( 0 ) s + 25 s I ( s ) = 0 4 I ( s ) + s I ( s ) + 25 s I ( s ) = − 20 s + v ( 0 ) s + 40 s I ( s ) [ 4 + s + 25 s ] = − 20 s + v ( 0 ) s + 40 s I ( s ) [ 4 s + s 2 + 25 s ] = − 20 s + v ( 0 ) s + 40 s Substitute 20 for v ( 0 ) in above equation. I ( s ) [ 4 s + s 2 + 25 s ] = − 20 s + 20 s + 40 s I ( s ) [ s 2 + 4 s + 25 s ] = 40 s Simplify the above equation to find I ( s ) . I ( s ) = 40 s ( s s 2 + 4 s + 25 ) I ( s ) = 40 s 2 + 4 s + 25 (4) From the equation (4), the characteristic equation is s 2 + 4 s + 25 = 0 (5) Write a general expression to calculate the roots of quadratic equation ( a s 2 + b s + c = 0 ) . s 1 , 2 = − b ± b 2 − 4 a c 2 a (6) Comparing the equation (5) with the equation ( a s 2 + b s + c = 0 ) . a = 1 b = 4 c = 25 Substitute 1 for a , 4 for b , and 25 for c in equation (6) to find s 1 , 2 . s 1 , 2 = − 4 ± ( 4 ) 2 − 4 ( 1 ) ( 25 ) 2 ( 1 ) = − 4 ± 16 − 100 2 ( 1 ) = − 4 ± − 84 2 = − 4 ± j 9.1652 2 Simplify the above equation to find s 1 , 2 . s 1 , 2 = − 4 + j 9.1652 2 , − 4 − j 9.1652 2 = − 2 + j 4.5826 , − 2 − j 4.5826 Substitute the roots of characteristic equation in equation (4) to find V ( s ) . I ( s ) = 40 ( s − ( − 2 + j 4.5826 ) ) ( ( s − ( − 2 − j 4.5826 ) ) ) = 40 ( s − ( − 2 + j 4.5826 ) ) ( s − ( − 2 − j 4.5826 ) ) Take partial fraction for above equation

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 16, Problem 39P

To determine

Find the expression of current i(t) for t>0 in the circuit of Figure 16.62.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 38P

Chapter 16, Problem 40P

Students have asked these similar questions

1) Compute the voltages at each receiver branch (Vo ad V₁ see block diagram next page) for each of the possible transmitted signals: Transmitted signals are generated as shown below: Binary wave in unipolar form (a) With basis functions: Inverter 41(t) Product modulator Product modulator 42(t) BFSK + signal + Si(t) P1(t)= √Eb = cos (2лfit+0₁) $2(t) 42(t)= √Eb 层 cos (2лf2t+ t+02) Generating signals: 2E Si(t) cos (2лfit+0₁), bit=0 Ть SBFSK (t) 2E |$2(t)= cos (2лf2t+02), bit=1

Find the disruptive voltage and visual corona voltage for 3-phase line consisting of 2.5 cm diameter conductor spaced equilateral triangular formation of 4 m. The following data can be assumed, temperature 25°c, pressure 73 cm of mercury, surface factor 0.84, irregularity factor 0.72.

A 3-phase, 4-wire distributor supplies a balanced voltage of 400/230 V to a load consisting of 8 A at p.f. 0-7 lagging for R-phase, 10 A at p.f. 0-8 leading for Y phase and 12 A at unity p.f. for B phase. The resistance of each line conductor is 0.4 2. The reactance of neutral is 0.2 2. Calculate the neutral current, the suppl voltage for R phase and draw the phasor diagram. The phase sequence is RYB. VR Phasor diagram

Chapter 16 Solutions

Fundamentals of Electric Circuits

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...

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 expression of current i ( t ) for t > 0 in the circuit of Figure 16.62.

Solution Summary: The author explains the formula used to calculate the impedance of a resistor in s -domain.

Videos

Find the expression of current i(t) for t>0 in the circuit of Figure 16.62.

Want to see the full answer?

Chapter 16 Solutions

Find the expression of current i ( t ) for t &gt; 0 in the circuit of Figure 16.62.

Solution Summary: The author explains the formula used to calculate the impedance of a resistor in s -domain.

Videos

Find the expression of current i(t) for t>0 in the circuit of Figure 16.62.

Want to see the full answer?

Chapter 16 Solutions

Find the expression of current i ( t ) for t > 0 in the circuit of Figure 16.62.