### Problem Statement:**Find the values indicated below for the following circuit:****Given Circuit Diagram:**- A power supply of 10V connected in series with a resistor of 10KΩ and a switch.- The switch has two positions: Position 1 and Position 2.- In Position 1, the circuit includes an additional path through a 20KΩ resistor and a capacitor (10μF) in parallel.- The variables of interest are: \(i_c\), \(V_C\), and \(\tau\).**When the switch is in Position 1:**- \(i_c =\)- \(V_C =\)- \(\tau =\)**When the switch is in Position 2:**- Assume the circuit is in steady state when the switch is closed.- \(i_c =\)- \(V_C =\)- \(\tau =\)### Explanation:**Circuit Diagram Breakdown:**- **Power Source:** 10V- **Resistors:** 10KΩ and 20KΩ- **Capacitor:** 10μF- **Key Variables:** - \(i_c:\) The current through the capacitor. - \(V_C:\) The voltage across the capacitor. - \(\tau:\) The time constant of the circuit.### Analysis Steps:1. **Switch in Position 1:** - Determine the current through the capacitor, \(i_c\). - Calculate the voltage across the capacitor, \(V_C\). - Compute the time constant of the circuit, \(\tau\).2. **Switch in Position 2:** - Re-calculate the current through the capacitor, \(i_c\). - Determine the voltage across the capacitor, \(V_C\). - Compute the time constant of the circuit, \(\tau\), under steady state conditions.This problem requires knowledge of capacitive circuits, Kirchhoff’s voltage and current laws, and the time constant formula (\(\tau = R_{\text{eq}} \times C\)) where \(R_{\text{eq}}\) is the equivalent resistance seen by the capacitor. Students should perform these computations step-by-step to find the desired values for both switch positions. ### Example Problem from Electrical Engineering**Problem 6:****a) Determine the time constant of the circuit.****b) Sketch the waveforms for \( v_C \) and \( i_C \).**#### Circuit Description:The circuit consists of a 10V power source connected in series with a 30µF capacitor and a 10kΩ resistor.- **Capacitor (\(C\))**: 30µF- **Resistor (\(R\))**: 10kΩ- **Voltage Source**: 10V DC#### Explanation for Problem Solution:1. **Time Constant Calculation:** The time constant (\(\tau\)) of an RC circuit is calculated using the formula: \[ \tau = R \times C \] - Given: - \(R = 10kΩ = 10,000Ω\) - \(C = 30µF = 30 \times 10^{-6} F\) - Therefore: \[ \tau = 10,000Ω \times 30 \times 10^{-6} F = 0.3 \text{ seconds} \]2. **Waveform Sketch:** - **Voltage across the capacitor (\( v_C \))**: As the circuit is charged, the voltage across the capacitor follows the equation: \[ v_C(t) = V_{source} \left(1 - e^{-\frac{t}{\tau}}\right) \] This represents an exponential grow towards the supply voltage over time, reaching 63% of the final value (10V) after one time constant (\(\tau\)). - **Current through the capacitor (\( i_C \))**: The current through the capacitor at time \(t\) is given by: \[ i_C(t) = \frac{V_{source}}{R} \cdot e^{-\frac{t}{\tau}} \] This shows an exponential decay from an initial peak value, reaching 37% of its initial value after one time constant (\(\tau\)). By understanding these equations and the behavior of the elements, students can correctly sketch the waveforms for \( v_C \) and \( i_C \).

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5,-Find the values indieated · below For the tol circuit. l 20K when switch is in lov JOV 10uF Ne ビニ when switch is in position 2, Assume the circuit is in steady state when this Switch is closed.

5,-Find the values indieated · below For the tol circuit. l 20K when switch is in lov JOV 10uF Ne ビニ when switch is in position 2, Assume the circuit is in steady state when this Switch is closed.

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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