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Using the diagram below, find the time constant τ for the circuit when it has its capacitor filled up to two different starting values, and then are discharged.  During the first run, it will take 34ms to reach 7.3nC, and for the second run, it will take twice the starting charge, and take 76ms to reach 7.3nC.

Using the diagram below, find the time constant τ for the circuit when it has its capacitor filled up to two different starting values, and then are discharged.  During the first run, it will take 34ms to reach 7.3nC, and for the second run, it will take twice the starting charge, and take 76ms to reach 7.3nC.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Exercise 2 from Chapter 6 (part c)

Using the diagram below, find the time constant τ for the circuit when it has its capacitor filled up to two different starting values, and then are discharged.  During the first run, it will take 34ms to reach 7.3nC, and for the second run, it will take twice the starting charge, and take 76ms to reach 7.3nC.

 

The image depicts an electrical circuit diagram consisting of a battery \( \mathcal{E} \), a switch (shown as a simple line gap), and three resistors: \( R_1 \), \( R_2 \), and \( R_3 \). The resistors are arranged in a combination of series and parallel configurations. ### Description of the Diagram 1. **Battery (\( \mathcal{E} \))**: Positioned on the left-hand side, it provides the electromotive force for the circuit. 2. **Switch**: Located near the battery, represented as an open gap in the line indicating the switch could be open or closed to control the current flow. 3. **Resistor \( R_1 \)**: This resistor is connected in series with the battery and the point labeled \( A \). 4. **Resistors \( R_2 \) and \( R_3 \)**: These two resistors are connected in parallel with each other. The connection begins from the node labeled \( B \). \( R_2 \) connects from \( B \) to \( C \), and \( R_3 \) connects from \( B \) directly back to the lower side of the battery. 5. **Circuit Nodes**: - **Node A** is connected to \( R_1 \). - **Node B** is where \( R_1 \) and both \( R_2 \) and \( R_3 \) meet. - **Node C** connects \( R_2 \) back to the loop completing the path. ### Current Flow - **Current \( I \)** flows from the positive terminal of the battery through \( R_1 \), continuing to node \( B \), then it splits between \( R_2 \) (to node \( C \)) and \( R_3 \), eventually combining back before reaching the negative terminal of the battery. This circuit is exemplary of a basic mixed-series-parallel resistor circuit allowing for analysis of current distribution across various components and the total resistance of the circuit.
Transcribed Image Text:The image depicts an electrical circuit diagram consisting of a battery \( \mathcal{E} \), a switch (shown as a simple line gap), and three resistors: \( R_1 \), \( R_2 \), and \( R_3 \). The resistors are arranged in a combination of series and parallel configurations. ### Description of the Diagram 1. **Battery (\( \mathcal{E} \))**: Positioned on the left-hand side, it provides the electromotive force for the circuit. 2. **Switch**: Located near the battery, represented as an open gap in the line indicating the switch could be open or closed to control the current flow. 3. **Resistor \( R_1 \)**: This resistor is connected in series with the battery and the point labeled \( A \). 4. **Resistors \( R_2 \) and \( R_3 \)**: These two resistors are connected in parallel with each other. The connection begins from the node labeled \( B \). \( R_2 \) connects from \( B \) to \( C \), and \( R_3 \) connects from \( B \) directly back to the lower side of the battery. 5. **Circuit Nodes**: - **Node A** is connected to \( R_1 \). - **Node B** is where \( R_1 \) and both \( R_2 \) and \( R_3 \) meet. - **Node C** connects \( R_2 \) back to the loop completing the path. ### Current Flow - **Current \( I \)** flows from the positive terminal of the battery through \( R_1 \), continuing to node \( B \), then it splits between \( R_2 \) (to node \( C \)) and \( R_3 \), eventually combining back before reaching the negative terminal of the battery. This circuit is exemplary of a basic mixed-series-parallel resistor circuit allowing for analysis of current distribution across various components and the total resistance of the circuit.
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