Explanation Calculation: The given diagram is shown in Figure 1. The conversion from μ F into F is given by, 1 μ F = 10 − 6 F The conversion of 100 μ F in to F is given by, 100 μ F = 100 × 10 − 6 F The switch is closed at t > 0 . The required diagram is shown in Figure 2. Apply KVL in the above circuit. − 20 sin ( 100 t ) + ( 1 ) d i ( t ) d t + 400 i ( t ) + 1 100 × 10 − 6 ∫ i ( t ) d t = 0 d 2 i ( t ) d t 2 + 400 i ( t ) + 10 4 ∫ i ( t ) d t = 20 sin ( 100 t ) Differentiate the above equation with respect to t . d 2 i ( t ) d t 2 + 400 d i d t + 10000 i ( t ) = 20 ( 100 ) cos ( 100 t ) ........ (1) The general expression for the differential equation is given by, d 2 i p ( t ) d t 2 + 2 α d i p ( t ) d t + ω 0 2 i p ( t ) = f ( t ) ......... (2) The equation for the particular integral is given by, i p ( t ) = A cos ( 100 t ) + B sin ( 100 t ) ......... (3) Substitute A cos ( 100 t ) + B sin ( 100 t ) for i p ( t ) , 400 for 2 α , 2 , 000 cos ( 100 t ) for f ( t ) and 10 , 000 for ω 0 2 i p ( t ) in equation (2). [ − A ( 10 4 ) cos ( 100 t ) + − B ( 10 4 ) sin ( 100 t ) + 400 [ − A ( 100 ) sin ( 100 t ) + B ( 100 ) cos ( 100 t ) ] + ( 10 4 ) [ A cos ( 100 t ) + B sin ( 100 t ) ] ] = 2 , 000 cos ( 100 t ) The coefficients of sine terms is calculated as, − B ( 10 4 ) + A ( 100 ) ( 400 ) + 10 4 B = 0 − A ( 100 ) ( 400 ) = 0 A = 0 The coefficients of cosine terms is calculated as, − A ( 10 4 ) + B ( 100 ) ( 00 ) + 10 4 A = 2 , 000 − ( 0 ) ( 10 4 ) + B ( 100 ) ( 400 ) + ( 10 4 ) ( 0 ) = 2000 B = 2 , 000 ( 100 ) ( 400 ) B = 0.05 Substitute 0.05 for B and 0 for A in equation i p ( t ) = ( 0 ) cos ( 100 t ) + 0.05 sin ( 100 t ) = 0.05 sin ( 100 t ) The attenuation constant α is calculated as, α = R 2 L Substitute 400 Ω for R and 1 H for L in the above equation. α = 400 2 ( 1 ) = 200 The natural frequency is calculated as, ω 0 = 1 L C Substitute 100 × 10 − 6 F for C and 1 H for L in the above equation. ω 0 = 1 ( 1 ) ( 100 × 10 − 6 ) = 100 The damping ratio is calculated as, ξ = α ω 0 Substitute 100 for ω 0 and 200 for α in the above equation. ξ = 200 100 = 2 The expression for the complementary solution is given by, i c ( t ) = K 1 e − s 1 t + K 2 e − s 2 t

7th Edition

ISBN: 8220106714201

Author: HAMBLEY

Publisher: YUZU

See similar textbooks

Concept explainers

Capacitor

The capacitor is an element used to store electrical energy in the electrical field. A capacitor is a form of passive energy.

Videos

Question

Chapter 4, Problem 4.69P

To determine

The expression for i(t) for t>0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 4.68P

Chapter 4, Problem 4.70P

Students have asked these similar questions

Three speech signals are TDM multiplexed with a high-quality music signal. If each speech signal is sampled at 16 kHz and PCM quantized by 8 bits/sample, while the music signal is sampled at 64 kHz with the same PCM quantizer. 1. Draw the block diagram of this TDM. 2. Calculate the output bit rate of this TDM.

You and your crew have made it through the night and the day has brought more warmth. After searching the industrial site, you find an abundant amount of fuel to run the generators to keep you warm. You also find a memory card labelled “cure”, but your cell phone battery is dead. First things first, you will need to stay safe as the zombies continue to hunt you in your current location. The industrial site is surrounded by a metal chain-link fence. You decide you will electrify the fence to keep the zombies from scaling it. But the output voltage from the generators is not high enough to really deter them. You would like to apply around 10 kV to the fence (AC or DC, at that voltage it doesn’t really matter). You find a transformer that you can use but it only has a turn ratio of 10. You find some diodes and capacitors and construct the circuit shown in Figure 3 with the intention of hooking Vout to the fence. Perform a simulation, displaying the voltage Vout using a scope.…

Please answer all questions 1. Calculate the magnitude (in RMS) of the current through R1 2. Calculate the magnitude (in RMS) of the current through R2. Simulation 1. Construct the circuit in Figure 2 in the Circuit JS simulator. Note that transformers in Circuit JS may be unstable. It is suggested to draw them by clicking from the bottom left corner to the top right corner and refresh your simulation before taking a measurement. 2. Perform a simulation, displaying the voltage across the voltage source, the current through R1, and the current through R2 in a “stacked” scope. Display the RMS average for each trace. Include a screenshot. Analysis 1. Compare the simulation results for the currents through R1 and R2. What is the percentage difference between the calculated and simulated value for each? Comment on why there may be a discrepancy.

Chapter 4 Solutions

EBK ELECTRICAL ENGINEERING

Ch. 4 - Suppose we have a capacitance C discharging...Ch. 4 - The dielectric materials used in real capacitors...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - A 100F capacitance is initially charged to 1000 V....Ch. 4 - At t = 0, a charged 10{ F capacitance is connected...Ch. 4 - At time t1 , a capacitance C is charged to a...Ch. 4 - Given an initially charged capacitance that begins...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - In physics, the half-life is often used to...Ch. 4 - We know that a 50F capacitance is charged to an...

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.