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Find the equivalent capacitance, CAB , between terminals A and B in the circuit shown below. Hint: since simplification through combining series or parallel capacitors is not possible, consider adding a %3! test source as we did to find equivalent resistance except we'll calculate CAB = QA/VAB- Use the results from problem 3 to determine the voltage across terminals A and B, and to determine the charge stored at node A by summing the charge across the capacitors connected to node A. A 2 µF 1 µF CAB 1 µF 1 µF 2 µF

Find the equivalent capacitance, CAB , between terminals A and B in the circuit shown below. Hint: since simplification through combining series or parallel capacitors is not possible, consider adding a %3! test source as we did to find equivalent resistance except we'll calculate CAB = QA/VAB- Use the results from problem 3 to determine the voltage across terminals A and B, and to determine the charge stored at node A by summing the charge across the capacitors connected to node A. A 2 µF 1 µF CAB 1 µF 1 µF 2 µF

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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Please solve question for equivalence, other circuit is pictured to show what the problem is asking 

**Title:** Analyzing Capacitor Voltages Using Nodal Analysis **Objective:** Understand how to find the voltages across each capacitor in a given electrical circuit using nodal analysis. **Instructions:** Examine the circuit and identify the components and nodes. In the circuit, identify: - A voltage source of 5V. - Four capacitors with the following capacitances: 2µF, 1µF, 1µF, and 2µF. **Circuit Description:** - **Nodes:** The circuit is divided into distinct nodes labeled A, B, C, and D. - **Capacitors:** - Between nodes A and C: 2µF - Between nodes C and B: 1µF - Between nodes A and D: 1µF - Between nodes D and B: 2µF **Procedure:** 1. **Grounding:** - Ground Node B. 2. **Nodal Analysis:** - Use the given hint and apply Nodal Analysis by considering the charge leaving each node. Here, charge \( Q \) is defined as \( Q = CV \), where \( C \) is the capacitance and \( V \) is the voltage. - Formulate equations based on this principle. For instance, at node C: \[ 2\mu F(V_C - V_A) + 1\mu F(V_C - 0) + 1\mu F(V_C - V_D) = 0 \] 3. **Calculate:** Solve these simultaneous equations to find unknown node voltages. **Outcome:** This procedure will allow you to calculate the voltage across each capacitor using node voltages derived from the nodal analysis equations. **Conclusion:** Applying nodal analysis to capacitive circuits can effectively determine the voltage across each component, aiding in understanding circuit behavior and design.
Transcribed Image Text:**Title:** Analyzing Capacitor Voltages Using Nodal Analysis **Objective:** Understand how to find the voltages across each capacitor in a given electrical circuit using nodal analysis. **Instructions:** Examine the circuit and identify the components and nodes. In the circuit, identify: - A voltage source of 5V. - Four capacitors with the following capacitances: 2µF, 1µF, 1µF, and 2µF. **Circuit Description:** - **Nodes:** The circuit is divided into distinct nodes labeled A, B, C, and D. - **Capacitors:** - Between nodes A and C: 2µF - Between nodes C and B: 1µF - Between nodes A and D: 1µF - Between nodes D and B: 2µF **Procedure:** 1. **Grounding:** - Ground Node B. 2. **Nodal Analysis:** - Use the given hint and apply Nodal Analysis by considering the charge leaving each node. Here, charge \( Q \) is defined as \( Q = CV \), where \( C \) is the capacitance and \( V \) is the voltage. - Formulate equations based on this principle. For instance, at node C: \[ 2\mu F(V_C - V_A) + 1\mu F(V_C - 0) + 1\mu F(V_C - V_D) = 0 \] 3. **Calculate:** Solve these simultaneous equations to find unknown node voltages. **Outcome:** This procedure will allow you to calculate the voltage across each capacitor using node voltages derived from the nodal analysis equations. **Conclusion:** Applying nodal analysis to capacitive circuits can effectively determine the voltage across each component, aiding in understanding circuit behavior and design.
To find the equivalent capacitance, \( C_{AB} \), between terminals A and B in the circuit shown, follow these guidelines. **Hint:** Since simplification through combining series or parallel capacitors is not possible, consider adding a test source as used to find equivalent resistance. However, in this case, calculate \( C_{AB} = Q_A/V_{AB} \). Use the results from problem 3 to determine the voltage across terminals A and B. Also, determine the charge stored at node A by summing the charges across the capacitors connected to node A. ### Circuit Diagram Details: - **Node A** is connected to a 2 µF capacitor on the left, connected directly to node C. - Node A is also connected to a 1 µF capacitor on the right, connected directly to node D. - Between nodes C and D is a 1 µF capacitor. - Node C is connected to node B via another 1 µF capacitor. - Node D is connected to node B via a 2 µF capacitor. The diagram displays a network of capacitors forming a bridge configuration, where straightforward series or parallel calculations are not possible. An analytical approach involving charge distribution and voltage analysis is advised.
Transcribed Image Text:To find the equivalent capacitance, \( C_{AB} \), between terminals A and B in the circuit shown, follow these guidelines. **Hint:** Since simplification through combining series or parallel capacitors is not possible, consider adding a test source as used to find equivalent resistance. However, in this case, calculate \( C_{AB} = Q_A/V_{AB} \). Use the results from problem 3 to determine the voltage across terminals A and B. Also, determine the charge stored at node A by summing the charges across the capacitors connected to node A. ### Circuit Diagram Details: - **Node A** is connected to a 2 µF capacitor on the left, connected directly to node C. - Node A is also connected to a 1 µF capacitor on the right, connected directly to node D. - Between nodes C and D is a 1 µF capacitor. - Node C is connected to node B via another 1 µF capacitor. - Node D is connected to node B via a 2 µF capacitor. The diagram displays a network of capacitors forming a bridge configuration, where straightforward series or parallel calculations are not possible. An analytical approach involving charge distribution and voltage analysis is advised.
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