Explanation Given data: Refer to Figure 16.77 in the textbook. The switch is in position 1 for t < 0 . The switch is at the top of the capacitor at time t = 0 . 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 when the switch is in position ‘1’ 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 resistors R 1 and R 2 are connected in series. The current through the inductor is calculated as follows: i L ( 0 − ) = 120 V 4 Ω + 16 Ω = 120 V 20 Ω = 6 A Refer to Figure 2, there is no capacitor placed in the circuit. Therefore, the voltage across the capacitor is zero. v C ( 0 − ) = 0 V The current through inductor and voltage across capacitor is always continuous so that, i ( 0 ) = i L ( 0 − ) = i L ( 0 + ) = 6 A v ( 0 ) = v C ( 0 − ) = v C ( 0 + ) = 0 V For time t > 0 , the switch is moved from position ‘1’ to the top of the capacitor. Now the Figure 1 is reduced as shown in Figure 3. Substitute 16 Ω for R 2 in equation (1) to find Z R 2 . Z R 2 = 16 Substitute 4 H for L in equation (2) to find Z L . Z L = s ( 4 H ) = 4 s Substitute 1 16 F for C in equation (3) to find Z C . Z C = 1 s ( 1 16 F ) = 16 s Using element transformation methods with initial conditions convert the Figure 3 into s -domain. Apply Kirchhoff’s voltage law for the circuit shown in Figure 4. 16 s I ( s ) + 4 s I ( s ) − ( 4 s ) i ( 0 ) s + 16 I ( s ) = 0 16 s I ( s ) + 4 s I ( s ) − 4 i ( 0 ) + 16 I ( s ) = 0 I ( s ) [ 16 s + 4 s + 16 ] = 4 i ( 0 ) I ( s ) [ 16 + 4 s 2 + 16 s s ] = 4 i ( 0 ) Substitute 6 for i ( 0 ) in above equation

6th Edition

ISBN: 8220102801448

Author: Alexander

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 16, Problem 54P

To determine

Find the expression of voltage $v(t)$ for $t>0$ in the circuit of Figure 16.77.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 53P

Chapter 16, Problem 55P

Students have asked these similar questions

SIM1 RESET O SIMULINO ARDUINO AREF 13 12 -11 www.arduino.cc blogembarcado.blogspot.com SIMULINO UNO BUZ1 BUZZER R1 R2 51.1 68.1 GAS1 MQ-2 GAS SENSOR MQ-2 TestPin www.TheEng Vcc OUT GND Can the expt help me write Arduino code for the Project sensou pas?

Solve this problem and show all of the work

Chapter 16 Solutions

EBK 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 voltage v ( t ) for t > 0 in the circuit of Figure 16.77.

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

Videos

Find the expression of voltage $v(t)$ for $t>0$ in the circuit of Figure 16.77.

Want to see the full answer?

Chapter 16 Solutions

Find the expression of voltage v ( t ) for t &gt; 0 in the circuit of Figure 16.77.

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

Videos

Find the expression of voltage v(t)<m:math><m:mrow><m:mi>v</m:mi><m:mrow><m:mo>(</m:mo><m:mi>t</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math> for t>0<m:math><m:mrow><m:mi>t</m:mi><m:mo>&gt;</m:mo><m:mn>0</m:mn></m:mrow></m:math> in the circuit of Figure 16.77.

Want to see the full answer?

Chapter 16 Solutions

Find the expression of voltage v ( t ) for t > 0 in the circuit of Figure 16.77.

Find the expression of voltage $v(t)$ for $t>0$ in the circuit of Figure 16.77.