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3. Given i () 1.5K L (1) 100 mh 0.01 μ f with input (changing from –5 to +5 at t=0) in (1) - 5 a. Find vc(0+) and i (0+) if the circuit is in the steady state when the input changes at time t=0 from – 5 volts to +5 volts b. Write the differential equation for vc(t) for t 2 0 by writing and then taking the derivative of the node equation at node 1 c. Find vc (0+) + +1

3. Given i () 1.5K L (1) 100 mh 0.01 μ f with input (changing from –5 to +5 at t=0) in (1) - 5 a. Find vc(0+) and i (0+) if the circuit is in the steady state when the input changes at time t=0 from – 5 volts to +5 volts b. Write the differential equation for vc(t) for t 2 0 by writing and then taking the derivative of the node equation at node 1 c. Find vc (0+) + +1

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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Help with a-d please

**Circuit Analysis Problem** **Given:** 1. **Circuit Diagram:** - Components: - Resistor: 1.5 kΩ - Inductor: 100 mH - Capacitor: 0.01 μF - Input Voltage Source: \( v_{in}(t) \) - Node voltages and currents: - \( i_R(t) \) through the resistor - \( i_L(t) \) through the inductor - \( v_C(t) \) across the capacitor 2. **Input Voltage Change:** The input \( v_{in}(t) \) switches from -5 volts to +5 volts at \( t = 0 \). 3. **Graph:** - The graph shows \( v_{in}(t) \) with a step change at \( t = 0 \), from -5 to +5 volts. --- **Tasks:** a. **Initial Conditions:** - Determine \( v_C(0^+) \) and \( i_L(0^+) \) assuming the circuit is in steady state just before \( t = 0 \). b. **Differential Equation for \( v_C(t) \):** - Derive the equation for \( v_C(t) \) for \( t \geq 0 \) by applying the node equation at node 1 and differentiating as necessary. c. **Initial Rate of Change:** - Calculate \( \dot{v}_C(0^+) \), the initial rate of change of the capacitor voltage. d. **Transient Response:** - Solve for \( v_C(t) \) and classify the transient response as overdamped, underdamped, or critically damped. --- This exercise involves applying electrical circuit analysis techniques to solve for the behavior of an RLC circuit when subjected to a step input. The analysis includes determining initial conditions, setting up differential equations, and analyzing the system's transient response.
Transcribed Image Text:**Circuit Analysis Problem** **Given:** 1. **Circuit Diagram:** - Components: - Resistor: 1.5 kΩ - Inductor: 100 mH - Capacitor: 0.01 μF - Input Voltage Source: \( v_{in}(t) \) - Node voltages and currents: - \( i_R(t) \) through the resistor - \( i_L(t) \) through the inductor - \( v_C(t) \) across the capacitor 2. **Input Voltage Change:** The input \( v_{in}(t) \) switches from -5 volts to +5 volts at \( t = 0 \). 3. **Graph:** - The graph shows \( v_{in}(t) \) with a step change at \( t = 0 \), from -5 to +5 volts. --- **Tasks:** a. **Initial Conditions:** - Determine \( v_C(0^+) \) and \( i_L(0^+) \) assuming the circuit is in steady state just before \( t = 0 \). b. **Differential Equation for \( v_C(t) \):** - Derive the equation for \( v_C(t) \) for \( t \geq 0 \) by applying the node equation at node 1 and differentiating as necessary. c. **Initial Rate of Change:** - Calculate \( \dot{v}_C(0^+) \), the initial rate of change of the capacitor voltage. d. **Transient Response:** - Solve for \( v_C(t) \) and classify the transient response as overdamped, underdamped, or critically damped. --- This exercise involves applying electrical circuit analysis techniques to solve for the behavior of an RLC circuit when subjected to a step input. The analysis includes determining initial conditions, setting up differential equations, and analyzing the system's transient response.
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