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find ic (0-), ic (0+), ic (), and the time constant, t. _Use this information to find K1 and K2 where ic (t) = K1 + K2 e-t/t for t> 0. Compare this to a calculation of ic(t) = C d(vc (t))/dt using vc (t)

find ic (0-), ic (0+), ic (), and the time constant, t. _Use this information to find K1 and K2 where ic (t) = K1 + K2 e-t/t for t> 0. Compare this to a calculation of ic(t) = C d(vc (t))/dt using vc (t)

Introductory Circuit Analysis (13th Edition)
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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Find \( i_c(0^-), i_c(0^+), i_c(\infty) \), and the time constant, \( \tau \). Use this information to find \( K_1 \) and \( K_2 \) where \( i_c(t) = K_1 + K_2 \, e^{-t/\tau} \) for \( t > 0 \). Compare this to a calculation of \[ \dot{i_c}(t) = C \, \frac{d(v_c(t))}{dt} \text{ using } v_c(t) \]
Transcribed Image Text:Find \( i_c(0^-), i_c(0^+), i_c(\infty) \), and the time constant, \( \tau \). Use this information to find \( K_1 \) and \( K_2 \) where \( i_c(t) = K_1 + K_2 \, e^{-t/\tau} \) for \( t > 0 \). Compare this to a calculation of \[ \dot{i_c}(t) = C \, \frac{d(v_c(t))}{dt} \text{ using } v_c(t) \]
**Circuit Analysis and Transient Response** In the circuit shown, the switch is initially closed. At time \( t = 0 \), the switch opens, disconnecting the 2 kΩ resistor and 150 μF capacitor from the circuitry to the left of the switch. You are tasked with finding and plotting \( v_C(t) \), the voltage across the capacitor, and \( i_O(t) \), the current through the 2 kΩ resistor and capacitor branch, after the switch opens. ### Circuit Description 1. **Components**: - Two resistors of 4 kΩ and 1 kΩ in series on the left. - A 2 kΩ resistor connected in parallel with a branch containing the 150 μF capacitor on the right. - A constant current source of 12 mA in the left branch before the switch. 2. **Configuration**: - Before \( t = 0 \), the circuit is closed, allowing the current to flow through the entire circuit, charging the capacitor. - At \( t = 0 \), the switch opens, isolating the right side containing the 2 kΩ resistor and capacitor from the rest. ### Objective: - **Find \( v_C(t) \)**: The voltage across the capacitor over time as it discharges through the 2 kΩ resistor. - **Find \( i_O(t) \)**: The current through the isolated 2 kΩ resistor and capacitor after the switch opens. This analysis involves solving differential equations to find the transient response of the RC circuit. The voltage and current plots will showcase the exponential decay typical of an RC discharge circuit.
Transcribed Image Text:**Circuit Analysis and Transient Response** In the circuit shown, the switch is initially closed. At time \( t = 0 \), the switch opens, disconnecting the 2 kΩ resistor and 150 μF capacitor from the circuitry to the left of the switch. You are tasked with finding and plotting \( v_C(t) \), the voltage across the capacitor, and \( i_O(t) \), the current through the 2 kΩ resistor and capacitor branch, after the switch opens. ### Circuit Description 1. **Components**: - Two resistors of 4 kΩ and 1 kΩ in series on the left. - A 2 kΩ resistor connected in parallel with a branch containing the 150 μF capacitor on the right. - A constant current source of 12 mA in the left branch before the switch. 2. **Configuration**: - Before \( t = 0 \), the circuit is closed, allowing the current to flow through the entire circuit, charging the capacitor. - At \( t = 0 \), the switch opens, isolating the right side containing the 2 kΩ resistor and capacitor from the rest. ### Objective: - **Find \( v_C(t) \)**: The voltage across the capacitor over time as it discharges through the 2 kΩ resistor. - **Find \( i_O(t) \)**: The current through the isolated 2 kΩ resistor and capacitor after the switch opens. This analysis involves solving differential equations to find the transient response of the RC circuit. The voltage and current plots will showcase the exponential decay typical of an RC discharge circuit.
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