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in the figure a potential difference of V-140 V is applied across a capacitor arrangement with capacitances C₁-9.80 uF. C₂-4.10. and C-14.2uF. What are (a) charge as. (b) potential difference Vs, and (c) stored energy Us for capacitor 3. (d) as-(e) v₁.and (f) U₁ for apacitor 1, and (g) 43. (h) V₂, and U₂ for capacitor 2

in the figure a potential difference of V-140 V is applied across a capacitor arrangement with capacitances C₁-9.80 uF. C₂-4.10. and C-14.2uF. What are (a) charge as. (b) potential difference Vs, and (c) stored energy Us for capacitor 3. (d) as-(e) v₁.and (f) U₁ for apacitor 1, and (g) 43. (h) V₂, and U₂ for capacitor 2

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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**Capacitor Circuit Analysis** In the figure, a potential difference of \( V = 140 \, \text{V} \) is applied across a capacitor arrangement with capacitances \( C_1 = 9.80 \, \mu\text{F} \), \( C_2 = 4.10 \, \mu\text{F} \), and \( C_3 = 12.4 \, \mu\text{F} \). **Questions to Consider:** 1. What are the charge \( q_3 \), potential difference \( V_3 \), and stored energy \( U_3 \) for capacitor 3? 2. Calculate the charge, potential difference, and stored energy for capacitors 1 and 2: - (a) \( q_1 \) and (b) \( V_1 \), (c) \( U_1 \) for capacitor 1 - (d) \( q_2 \) and (e) \( V_2 \), (f) \( U_2 \) for capacitor 2 **Diagram Explanation:** - The diagram shows a circuit where three capacitors (\( C_1 \), \( C_2 \), and \( C_3 \)) are arranged in a combination. - \( C_1 \) and \( C_2 \) are connected in series, and their combination is in parallel with \( C_3 \). **Analysis Steps:** 1. **Calculate Equivalent Capacitance:** - The series combination of \( C_1 \) and \( C_2 \) can be calculated as: \[ \frac{1}{C_{12}} = \frac{1}{C_1} + \frac{1}{C_2} \] - The total equivalent capacitance (\( C_{\text{eq}} \)) is the parallel combination of \( C_{12} \) and \( C_3 \): \[ C_{\text{eq}} = C_{12} + C_3 \] 2. **Determine Charge and Voltage:** - The charge across each capacitor (\( q_1, q_2, q_3 \)) and the potential difference across each can be determined using the capacitance-voltage relationship: \[ q = C \times V \]
Transcribed Image Text:**Capacitor Circuit Analysis** In the figure, a potential difference of \( V = 140 \, \text{V} \) is applied across a capacitor arrangement with capacitances \( C_1 = 9.80 \, \mu\text{F} \), \( C_2 = 4.10 \, \mu\text{F} \), and \( C_3 = 12.4 \, \mu\text{F} \). **Questions to Consider:** 1. What are the charge \( q_3 \), potential difference \( V_3 \), and stored energy \( U_3 \) for capacitor 3? 2. Calculate the charge, potential difference, and stored energy for capacitors 1 and 2: - (a) \( q_1 \) and (b) \( V_1 \), (c) \( U_1 \) for capacitor 1 - (d) \( q_2 \) and (e) \( V_2 \), (f) \( U_2 \) for capacitor 2 **Diagram Explanation:** - The diagram shows a circuit where three capacitors (\( C_1 \), \( C_2 \), and \( C_3 \)) are arranged in a combination. - \( C_1 \) and \( C_2 \) are connected in series, and their combination is in parallel with \( C_3 \). **Analysis Steps:** 1. **Calculate Equivalent Capacitance:** - The series combination of \( C_1 \) and \( C_2 \) can be calculated as: \[ \frac{1}{C_{12}} = \frac{1}{C_1} + \frac{1}{C_2} \] - The total equivalent capacitance (\( C_{\text{eq}} \)) is the parallel combination of \( C_{12} \) and \( C_3 \): \[ C_{\text{eq}} = C_{12} + C_3 \] 2. **Determine Charge and Voltage:** - The charge across each capacitor (\( q_1, q_2, q_3 \)) and the potential difference across each can be determined using the capacitance-voltage relationship: \[ q = C \times V \]
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