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#13: The switch has been open a long time (no current) and then closes at t = 0. Find the voltages v1 and v2, currents il and i2 each at the following three times: just before the switch closes, just after the switch closes and a long time after the switch closes. t=0 10 N 50 Ω ww 20 2 + 12 30 2 60 V ww

#13: The switch has been open a long time (no current) and then closes at t = 0. Find the voltages v1 and v2, currents il and i2 each at the following three times: just before the switch closes, just after the switch closes and a long time after the switch closes. t=0 10 N 50 Ω ww 20 2 + 12 30 2 60 V ww

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
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**Problem #13: Circuit Analysis** **Problem Statement:** The switch in the circuit has been open for a long time (resulting in no current flow) and then closes at time \( t = 0 \). Determine the voltages \( v_1 \) and \( v_2 \), and the currents \( i_1 \) and \( i_2 \) at three distinct times: 1. Just before the switch closes. 2. Immediately after the switch closes. 3. A long time after the switch closes. **Circuit Diagram Description:** - **Components:** - A switch that closes at \( t = 0 \). - A \( 30 \, \Omega \) resistor. - A \( 10 \, \Omega \) resistor in series with the \( 30 \, \Omega \) resistor. - A \( 50 \, \Omega \) resistor in parallel with the combination of the \( 10 \, \Omega \) and the \( 30 \, \Omega \) resistor. - A \( 20 \, \Omega \) resistor in parallel with the \( 50 \, \Omega \) resistor. - A \( 60 \, \text{V} \) DC voltage source. - Capacitors labeled \( C_1 \) and two nodes for voltage measurements, \( v_1 \) and \( v_2 \). - **Currents:** - \( i_1 \) flows through the \( 30 \, \Omega \) resistor and the parallel network. - \( i_2 \) flows through the \( 50 \, \Omega \) resistor. **Analysis Steps:** 1. **Before the Switch Closes:** - The circuit is open, so no current flows through it, and \( v_1 \) and \( v_2 \) need to be determined based on the initial conditions (capacitor voltages). 2. **Just After the Switch Closes:** - The circuit becomes active, allowing current to flow. The initial conditions of the voltages across the capacitors and the changes in current flows must be analyzed. 3. **A Long Time After the Switch Closes:** - The circuit reaches a steady state where the effects of the capacitors have stabilized. Analyze the currents and voltages in this steady state. This problem requires knowledge of
Transcribed Image Text:**Problem #13: Circuit Analysis** **Problem Statement:** The switch in the circuit has been open for a long time (resulting in no current flow) and then closes at time \( t = 0 \). Determine the voltages \( v_1 \) and \( v_2 \), and the currents \( i_1 \) and \( i_2 \) at three distinct times: 1. Just before the switch closes. 2. Immediately after the switch closes. 3. A long time after the switch closes. **Circuit Diagram Description:** - **Components:** - A switch that closes at \( t = 0 \). - A \( 30 \, \Omega \) resistor. - A \( 10 \, \Omega \) resistor in series with the \( 30 \, \Omega \) resistor. - A \( 50 \, \Omega \) resistor in parallel with the combination of the \( 10 \, \Omega \) and the \( 30 \, \Omega \) resistor. - A \( 20 \, \Omega \) resistor in parallel with the \( 50 \, \Omega \) resistor. - A \( 60 \, \text{V} \) DC voltage source. - Capacitors labeled \( C_1 \) and two nodes for voltage measurements, \( v_1 \) and \( v_2 \). - **Currents:** - \( i_1 \) flows through the \( 30 \, \Omega \) resistor and the parallel network. - \( i_2 \) flows through the \( 50 \, \Omega \) resistor. **Analysis Steps:** 1. **Before the Switch Closes:** - The circuit is open, so no current flows through it, and \( v_1 \) and \( v_2 \) need to be determined based on the initial conditions (capacitor voltages). 2. **Just After the Switch Closes:** - The circuit becomes active, allowing current to flow. The initial conditions of the voltages across the capacitors and the changes in current flows must be analyzed. 3. **A Long Time After the Switch Closes:** - The circuit reaches a steady state where the effects of the capacitors have stabilized. Analyze the currents and voltages in this steady state. This problem requires knowledge of
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