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Consider the circuit below. The capacitor has 61 uF capacitance. R1 has 36 kQ of resistance and R2 has 15 kO of resistance. The battery outputs 124 V. The value of R3 is irrelevant. The switch has been in the right position for a long time (long enough to fully charge the capacitor). At t = O s, the switch is flipped into the left position. Calculate the magnitude of the current through the capacitor att = 2.5 s, in units of mA. %3D R3 S1 R1 C1 V1+ R2

Consider the circuit below. The capacitor has 61 uF capacitance. R1 has 36 kQ of resistance and R2 has 15 kO of resistance. The battery outputs 124 V. The value of R3 is irrelevant. The switch has been in the right position for a long time (long enough to fully charge the capacitor). At t = O s, the switch is flipped into the left position. Calculate the magnitude of the current through the capacitor att = 2.5 s, in units of mA. %3D R3 S1 R1 C1 V1+ R2

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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(Please answer to the fourth decimal place - i.e 14.3225)

### Analyzing RC Circuit Behavior Consider the following circuit configuration, which includes a resistor-capacitor (RC) setup: - **Capacitor (C1)**: 61 µF capacitance - **Resistor R1**: 36 kΩ resistance - **Resistor R2**: 15 kΩ resistance - **Battery (V1)**: 124 V output - **Resistor R3**: Value irrelevant for this calculation The circuit features a switch (S1) that has been in the right position for an extended period, allowing the capacitor to become fully charged. At time \( t = 0 \) seconds, the switch is toggled to the left. The task is to determine the magnitude of the current flowing through the capacitor at time \( t = 2.5 \) seconds, expressed in milliamperes (mA). #### Circuit Diagram Description: The given circuit diagram consists of: - A battery (V1) providing 124V. - The capacitor (C1) placed in series with resistors \( R1 \) and \( R2 \), and the switch (S1) between them. - \( R3 \) connected in series with \( R2 \), whose value is irrelevant for this specific computation. - The switch (S1) initially connects the capacitor to the battery but is switched to left at \( t = 0 \), disconnecting the battery and connecting the capacitor to \( R2 \). ### Problem Solving To calculate the current through the capacitor at \( t = 2.5 \) seconds, follow these steps: 1. **Discharge Phase Analysis**: When the switch is flipped, the capacitor starts discharging through \( R2 \). The discharge current \( i(t) \) at any time \( t \) can be described by the equation: \[ i(t) = \frac{V_0}{R} e^{-\frac{t}{RC}} \] where: - \( V_0 \) is the initial voltage across the capacitor - \( R \) is the resistance in the discharge path - \( C \) is the capacitance of the capacitor - \( t \) is the time elapsed since the switch was flipped 2. **Initial Voltage \( V_0 \)**: Considering the capacitor was fully charged: \[
Transcribed Image Text:### Analyzing RC Circuit Behavior Consider the following circuit configuration, which includes a resistor-capacitor (RC) setup: - **Capacitor (C1)**: 61 µF capacitance - **Resistor R1**: 36 kΩ resistance - **Resistor R2**: 15 kΩ resistance - **Battery (V1)**: 124 V output - **Resistor R3**: Value irrelevant for this calculation The circuit features a switch (S1) that has been in the right position for an extended period, allowing the capacitor to become fully charged. At time \( t = 0 \) seconds, the switch is toggled to the left. The task is to determine the magnitude of the current flowing through the capacitor at time \( t = 2.5 \) seconds, expressed in milliamperes (mA). #### Circuit Diagram Description: The given circuit diagram consists of: - A battery (V1) providing 124V. - The capacitor (C1) placed in series with resistors \( R1 \) and \( R2 \), and the switch (S1) between them. - \( R3 \) connected in series with \( R2 \), whose value is irrelevant for this specific computation. - The switch (S1) initially connects the capacitor to the battery but is switched to left at \( t = 0 \), disconnecting the battery and connecting the capacitor to \( R2 \). ### Problem Solving To calculate the current through the capacitor at \( t = 2.5 \) seconds, follow these steps: 1. **Discharge Phase Analysis**: When the switch is flipped, the capacitor starts discharging through \( R2 \). The discharge current \( i(t) \) at any time \( t \) can be described by the equation: \[ i(t) = \frac{V_0}{R} e^{-\frac{t}{RC}} \] where: - \( V_0 \) is the initial voltage across the capacitor - \( R \) is the resistance in the discharge path - \( C \) is the capacitance of the capacitor - \( t \) is the time elapsed since the switch was flipped 2. **Initial Voltage \( V_0 \)**: Considering the capacitor was fully charged: \[
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