I have provided the answers for first three parts: Kindly solve for part d) e) and f)Q) An LC-circuit like the one shown in the figure contains an75.0-mH inductor and a 20-μF capacitor that initially carries a 200-μCcharge. The switch is thrown closed at t=0 seconds.a. Find the angular frequency (in rad/sec) of the resultingoscillation. A. 258 rad/sec B. 816 rad/sec C. 133 rad/sec D. 413 rad/secb. Find the frequency (in Hertz) of the resulting oscillation. A. 41.1 Hz B. 130 Hz C. 21.2 Hz D. 65.8 Hzc. What is the formula for the charge (in Coulombs) on the capacitor, Q(t), as a function of time.A. Q(t) = 7.50x10^-6 cos(21.2t)B. Q(t) = 413x10^-6 cos(130t)C. Q(t) = 200x10^-6 cos(816t)D. Q(t) = 133x10^-6 cos(39.8t)d. Write the formula for the current (in Amps) on the capacitor, I(t), as a function of time.A. I(t) = -75.0 sin (21.2 t)B. I(t) = -0.286 sin (816 t)C. I(t) = -0.163 sin ( 816t)D. I(t) = -2.33 sin (21.2 t) e. What is the maximum current this circuit will experience (Hint: look at your formula from Part d.)?A. Imax= 21.2 Amp B. Imax= 0.163 Amp C. Imax= 75.0 AmpD. Imax= 816 Ampf. At t = 1ms, find the charge (in μC) on the capacitor (Be sure your calculator is in radian mode).A. Q = 200 μC B. Q = 45.2 μC C. Q = 56.3 μC D. Q = 137 μC Please answer all the 3 parts d) e) and f). show all the work and every step. Thanks! ### LC Circuit with Initial Charge on Capacitor**Overview:**The diagram represents an LC circuit, a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected together.**Components:**1. **Capacitor (C):** - The capacitor is initially charged to a charge \( Q_0 \). This is represented by the positive (+++++) and negative (-----) signs on either side of the capacitor in the diagram.2. **Inductor (L):** - The inductor in the circuit is depicted as a series of coils or loops.3. **Switch:** - A switch is present in the circuit, labeled to close at \( t = 0 \).**Operation:**- At \( t = 0 \), the switch closes, allowing the current to flow through the circuit.- The initial charge \( Q_0 \) on the capacitor sets up an initial voltage across it.- As the circuit operates, the charge on the capacitor starts to discharge through the inductor and setup oscillations in the circuit due to the energy exchange between the capacitor’s electric field and the inductor’s magnetic field.### Diagram Analysis:- **Capacitor (C):** - Initially holds charge \( Q_0 \). - The positive and negative symbols indicate the presence of voltage across its plates.- **Inductor (L):** - Represented as a coil. - Inductance resists changes in current and creates a back EMF when current flows through it.- **Switch:** - Opens and closes the circuit. - In this scenario, the switch closes at \( t = 0 \), initiating the LC oscillation.### Educational Objective:This LC circuit is a fundamental component in the study of electrical engineering and electronics, demonstrating principles of oscillatory motion analogous to mechanical systems. The primary learning objectives include:- Understanding the oscillatory charge and current behavior in LC circuits.- Analyzing the energy transformation between the electric field in the capacitor and the magnetic field in the inductor.- Applying Kirchhoff’s voltage law in the context of time-varying circuits.This type of circuit is often used in filtering applications, radio transmitters, and signal processing to select specific frequency bands. Understanding the behavior of LC circuits is crucial for designing and analyzing resonant circuits in various electronic applications.

I have provided the answers for first three parts: Kindly solve for part d) e) and f) Q) An LC-circuit like the one shown in the figure contains an 75.0-mH inductor and a 20-μF capacitor that initially carries a 200-μC charge. The switch is thrown closed at t=0 seconds. a. Find the angular frequency (in rad/sec) of the resulting oscillation. A. 258 rad/sec B. 816 rad/sec C. 133 rad/sec D. 413 rad/sec b. Find the frequency (in Hertz) of the resulting oscillation. A. 41.1 Hz B. 130 Hz C. 21.2 Hz D. 65.8 Hz c. What is the formula for the charge (in Coulombs) on the capacitor, Q(t), as a function of time. A. Q(t) = 7.50x10^-6 cos(21.2t) B. Q(t) = 413x10^-6 cos(130t) C. Q(t) = 200x10^-6 cos(816t) D. Q(t) = 133x10^-6 cos(39.8t) d. Write the formula for the current (in Amps) on the capacitor, I(t), as a function of time. A. I(t) = -75.0 sin (21.2 t) B. I(t) = -0.286 sin (816 t) C. I(t) = -0.163 sin ( 816t) D. I(t) = -2.33 sin (21.2 t) e. What is the maximum current this circuit will experience (Hint: look at your formula from Part d.)? A. Imax= 21.2 Amp B. Imax= 0.163 Amp C. Imax= 75.0 Amp D. Imax= 816 Amp f. At t = 1ms, find the charge (in μC) on the capacitor (Be sure your calculator is in radian mode). A. Q = 200 μC B. Q = 45.2 μC C. Q = 56.3 μC D. Q = 137 μC Please answer all the 3 parts d) e) and f). show all the work and every step. Thanks!

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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I have provided the answers for first three parts: Kindly solve for part d) e) and f)

Q) An LC-circuit like the one shown in the figure contains an
75.0-mH inductor and a 20-μF capacitor that initially carries a 200-μC
charge. The switch is thrown closed at t=0 seconds.

a. Find the angular frequency (in rad/sec) of the resulting
oscillation.
A. 258 rad/sec B. 816 rad/sec C. 133 rad/sec D. 413 rad/sec

b. Find the frequency (in Hertz) of the resulting oscillation.
A. 41.1 Hz B. 130 Hz C. 21.2 Hz D. 65.8 Hz

c. What is the formula for the charge (in Coulombs) on the capacitor, Q(t), as a function of time.
A. Q(t) = 7.50x10^-6 cos(21.2t)

B. Q(t) = 413x10^-6 cos(130t)

C. Q(t) = 200x10^-6 cos(816t)

D. Q(t) = 133x10^-6 cos(39.8t)

d. Write the formula for the current (in Amps) on the capacitor, I(t), as a function of time.
A. I(t) = -75.0 sin (21.2 t)

B. I(t) = -0.286 sin (816 t)

C. I(t) = -0.163 sin ( 816t)

D. I(t) = -2.33 sin (21.2 t)

e. What is the maximum current this circuit will experience (Hint: look at your formula from Part d.)?
A. Imax= 21.2 Amp B. Imax= 0.163 Amp C. Imax= 75.0 Amp

D. Imax= 816 Amp

f. At t = 1ms, find the charge (in μC) on the capacitor (Be sure your calculator is in radian mode).

A. Q = 200 μC B. Q = 45.2 μC C. Q = 56.3 μC D. Q = 137 μC

Please answer all the 3 parts d) e) and f). show all the work and every step. Thanks!

### LC Circuit with Initial Charge on Capacitor

**Overview:**

The diagram represents an LC circuit, a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected together.

**Components:**

1. **Capacitor (C):**
- The capacitor is initially charged to a charge \( Q_0 \). This is represented by the positive (+++++) and negative (-----) signs on either side of the capacitor in the diagram.

2. **Inductor (L):**
- The inductor in the circuit is depicted as a series of coils or loops.

3. **Switch:**
- A switch is present in the circuit, labeled to close at \( t = 0 \).

**Operation:**

- At \( t = 0 \), the switch closes, allowing the current to flow through the circuit.
- The initial charge \( Q_0 \) on the capacitor sets up an initial voltage across it.
- As the circuit operates, the charge on the capacitor starts to discharge through the inductor and setup oscillations in the circuit due to the energy exchange between the capacitor’s electric field and the inductor’s magnetic field.

### Diagram Analysis:

- **Capacitor (C):**
- Initially holds charge \( Q_0 \).
- The positive and negative symbols indicate the presence of voltage across its plates.

- **Inductor (L):**
- Represented as a coil.
- Inductance resists changes in current and creates a back EMF when current flows through it.

- **Switch:**
- Opens and closes the circuit.
- In this scenario, the switch closes at \( t = 0 \), initiating the LC oscillation.

### Educational Objective:

This LC circuit is a fundamental component in the study of electrical engineering and electronics, demonstrating principles of oscillatory motion analogous to mechanical systems. The primary learning objectives include:

- Understanding the oscillatory charge and current behavior in LC circuits.
- Analyzing the energy transformation between the electric field in the capacitor and the magnetic field in the inductor.
- Applying Kirchhoff’s voltage law in the context of time-varying circuits.

This type of circuit is often used in filtering applications, radio transmitters, and signal processing to select specific frequency bands. Understanding the behavior of LC circuits is crucial for designing and analyzing resonant circuits in various electronic applications.

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