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Find Ceq 40 μF 50 μF 30 μF 10 μ 20 μF

Find Ceq 40 μF 50 μF 30 μF 10 μ 20 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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Hello, I started learning about Electrical circuits but got this exercise and I'm confused on how to solve it

**Problem:** Find the equivalent capacitance (\(C_{eq}\)) for the given circuit. **Circuit Configuration:** The circuit consists of five capacitors arranged in a combination of series and parallel connections: 1. A 40 µF capacitor in parallel with: - A series combination of a 30 µF capacitor and a 10 µF capacitor. 2. This entire arrangement is in parallel with two other capacitors: - A 50 µF capacitor. - A 20 µF capacitor. **Step-by-step Solution:** 1. **Series Combination (30 µF and 10 µF):** The formula for the equivalent capacitance (\(C_s\)) of capacitors in series is: \[ \frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} \] where \(C_1 = 30 \, \mu F\) and \(C_2 = 10 \, \mu F\). \[ \frac{1}{C_s} = \frac{1}{30} + \frac{1}{10} = \frac{1}{30} + \frac{3}{30} = \frac{4}{30} \] \[ C_s = \frac{30}{4} = 7.5 \, \mu F \] 2. **Parallel Combination with 40 µF Capacitor:** The total capacitance of parallel capacitors (\(C_p\)) is the sum of their capacitances: \[ C_p = 40 \, \mu F + 7.5 \, \mu F = 47.5 \, \mu F \] 3. **Final Parallel Combination with 50 µF and 20 µF Capacitors:** The overall equivalent capacitance (\(C_{eq}\)) with all capacitors in parallel is: \[ C_{eq} = 47.5 \, \mu F + 50 \, \mu F + 20 \, \mu F \] \[ C_{eq} = 117.5 \, \mu F \] **Conclusion:** The equivalent capacitance \(C_{eq}\) of the circuit is \(117.5 \,
Transcribed Image Text:**Problem:** Find the equivalent capacitance (\(C_{eq}\)) for the given circuit. **Circuit Configuration:** The circuit consists of five capacitors arranged in a combination of series and parallel connections: 1. A 40 µF capacitor in parallel with: - A series combination of a 30 µF capacitor and a 10 µF capacitor. 2. This entire arrangement is in parallel with two other capacitors: - A 50 µF capacitor. - A 20 µF capacitor. **Step-by-step Solution:** 1. **Series Combination (30 µF and 10 µF):** The formula for the equivalent capacitance (\(C_s\)) of capacitors in series is: \[ \frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} \] where \(C_1 = 30 \, \mu F\) and \(C_2 = 10 \, \mu F\). \[ \frac{1}{C_s} = \frac{1}{30} + \frac{1}{10} = \frac{1}{30} + \frac{3}{30} = \frac{4}{30} \] \[ C_s = \frac{30}{4} = 7.5 \, \mu F \] 2. **Parallel Combination with 40 µF Capacitor:** The total capacitance of parallel capacitors (\(C_p\)) is the sum of their capacitances: \[ C_p = 40 \, \mu F + 7.5 \, \mu F = 47.5 \, \mu F \] 3. **Final Parallel Combination with 50 µF and 20 µF Capacitors:** The overall equivalent capacitance (\(C_{eq}\)) with all capacitors in parallel is: \[ C_{eq} = 47.5 \, \mu F + 50 \, \mu F + 20 \, \mu F \] \[ C_{eq} = 117.5 \, \mu F \] **Conclusion:** The equivalent capacitance \(C_{eq}\) of the circuit is \(117.5 \,
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