Please help me, thank you so much. I have underlined what I thought the answer was. The questions are as follows:The switch in the following circuit closes at t = 0 (assume no initial charge on the capacitor). Determine the voltage, vC(t), and the current, iC(t), prior to the switch closing for t = 0‒ Vc(0-)= 0V because the initial charge is 0Ic(0-)= 0mA because there is no power supply Determine the vC(t) and iC(t) after the switch closes and after a long time (i.e. t = 0+ and t = ∞). Vc(0+)= 0V because the capacitor doesn’t charge instantaneously but increases exponentially.Ic(0+)= Current shoots up to 3.75 mAmps when the switch is closed. Vc(infinity) = asymptotic limit of 637 volts after increasing exponentially.Ic(infinity) = 0 mA after decreasing exponentially Determine the time constant, τ, for t > 0. τ=RC = (0.25uF)*(25.5k ohms) = 0.0063 Write out the equations for the voltage, vC(t), and the current, iC(t), for t > 0.Vc(t)= (637)V(1-e-(t/tau))Ic(t)= (3.75)mA(e-(t/tau)) thanks again! This image depicts an electrical circuit designed for educational purposes, particularly in studying transient response in circuits.**Components and Their Values:**1. **Resistors:** - A 30 kΩ resistor is placed on the left side of the circuit. - A 50 kΩ resistor is in series with a switch and is centrally located in the circuit. - A 120 kΩ resistor is included on the right side of the circuit.2. **Current Source:** - A current source provides a constant current of 25 mA, flowing upwards in the circuit.3. **Capacitor:** - A capacitor with a capacitance of 0.25 μF is placed in parallel with the 120 kΩ resistor. - The voltage across the capacitor is denoted as Vc, and the capacitor current is labeled as Ic (flowing downward).4. **Switch:** - There is a switch in series with the 50 kΩ resistor, and it is indicated that this switch closes at time t = 0.**Circuit Operation:**- Initially, the switch is open, and the circuit has a stable state.- At time t = 0, the switch closes, initiating a transient response in the circuit.- This change will affect the voltage Vc across the capacitor and the current Ic through the capacitor.This setup is typically used in exercises related to RC charging and discharging, allowing students to analyze how circuits respond to sudden changes in their configuration and to apply theories like Kirchhoff's laws and transient analysis equations.

The circuit is drawn as, Since the capacitor does not have any initial charges the voltage across the capacitor remains 0 as there is no power supply connected across the capacitor. The Current across the capacitor is also 0. For t<0,Vc(0-)=0 Vic(0-)=0 AWhen the switch is closed, the circuit becomes. at t=0+, The capacitor acts as short circuit, Vc(0+)=0 VThe current throught the capacitor is calculated using current division law, no current flows through 120 kΩ resistor,ic(0+)=25 mA×30 kΩ30 kΩ+50 kΩic(0+)=25 mA×30 80 ic(0+)=9.375 mA at t=∞, Finally the capacitor acts as open circuit, ic∞=0 A The current i in the circuit can be calculated as, i=25 mA×30 kΩ170 kΩ+30 kΩi=25 mA×30 200 i=30 8 mA The Voltage across the capacitor is the voltage across the 120 kilo ohm resistance. Vc∞=308 mA×120 kΩVc∞=450 VR=120 kΩ×80 kΩ120 kΩ+80 kΩR=48 kΩτ=RCC=0.25 μFC=0.25×10-6 Fτ=48 kΩ×0.25×10-6 Fτ=12×10-3 s For t>0, Vc(t)=V∞+V0+-V∞e-tτVc(t)=450 V+0-450e-tτVc(t)=4501-e-t0.012 Vic(t)=CdVc(t)dtic(t)=25×10-6×d(4501-e-t0.012dtic(t)=25×10-6×450×d1-e-t0.012dtic(t)=25×10-6×450×d-e-t0.012dtic(t)=25×10-6×450×e-t0.012×10.012ic(t)=11.25×10-3×e-t0.012×112×10-3ic(t)=0.9375×e-t0.012 A

Answered: Please help me, thank you so much. I…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Please help me, thank you so much. I have underlined what I thought the answer was. The questions are as follows:

The switch in the following circuit closes at t = 0 (assume no initial charge on the capacitor).

Determine the voltage, vC(t), and the current, iC(t), prior to the switch closing for t = 0‒

Vc(0-)= 0V because the initial charge is 0

Ic(0-)= 0mA because there is no power supply

Determine the vC(t) and iC(t) after the switch closes and after a long time (i.e. t = 0+ and t = ∞).

Vc(0+)= 0V because the capacitor doesn’t charge instantaneously but increases exponentially.

Ic(0+)= Current shoots up to 3.75 mAmps when the switch is closed.

Vc(infinity) = asymptotic limit of 637 volts after increasing exponentially.

Ic(infinity) = 0 mA after decreasing exponentially

Determine the time constant, τ, for t > 0.

τ=RC = (0.25uF)*(25.5k ohms) = 0.0063

Write out the equations for the voltage, vC(t), and the current, iC(t), for t > 0.

Vc(t)= (637)V(1-e-(t/tau))

Ic(t)= (3.75)mA(e-(t/tau))

thanks again!

This image depicts an electrical circuit designed for educational purposes, particularly in studying transient response in circuits.

**Components and Their Values:**

1. **Resistors:**
- A 30 kΩ resistor is placed on the left side of the circuit.
- A 50 kΩ resistor is in series with a switch and is centrally located in the circuit.
- A 120 kΩ resistor is included on the right side of the circuit.

2. **Current Source:**
- A current source provides a constant current of 25 mA, flowing upwards in the circuit.

3. **Capacitor:**
- A capacitor with a capacitance of 0.25 μF is placed in parallel with the 120 kΩ resistor.
- The voltage across the capacitor is denoted as Vc, and the capacitor current is labeled as Ic (flowing downward).

4. **Switch:**
- There is a switch in series with the 50 kΩ resistor, and it is indicated that this switch closes at time t = 0.

**Circuit Operation:**
- Initially, the switch is open, and the circuit has a stable state.
- At time t = 0, the switch closes, initiating a transient response in the circuit.
- This change will affect the voltage Vc across the capacitor and the current Ic through the capacitor.

This setup is typically used in exercises related to RC charging and discharging, allowing students to analyze how circuits respond to sudden changes in their configuration and to apply theories like Kirchhoff's laws and transient analysis equations.

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