### Educational Resource: Capacitor Circuits---#### Analysis of a Capacitor Circuit**Problem:**Shown in the circuit below is a battery providing 12 V voltage to a circuit of capacitors.1. **Find the equivalent capacitance of the combination of capacitors in the circuit.**2. **What charge flows through the battery as the capacitors are being charged?****Circuit Diagram:**- The circuit contains a battery with a voltage of 12 V.- There are three capacitors in the circuit: - Capacitor 1: 3.0 µF - Capacitor 2: 5.0 µF - Capacitor 3: 1.0 µFThe capacitors are arranged as follows based on the provided circuit:- Capacitor 1 (3.0 µF) is in series with a parallel combination of Capacitor 2 (5.0 µF) and Capacitor 3 (1.0 µF).**Steps to Solve:**1. **Find the equivalent capacitance of the parallel capacitors (5.0 µF and 1.0 µF):** In parallel, capacitances add up directly: \[ C_{\text{parallel}} = C_2 + C_3 = 5.0 \, \mu\text{F} + 1.0 \, \mu\text{F} = 6.0 \, \mu\text{F} \]2. **Determine the overall equivalent capacitance of the series combination:** The capacitors are now a series combination of 3.0 µF and 6.0 µF. The formula for capacitors in series is: \[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_{\text{parallel}}} \] Substituting the values: \[ \frac{1}{C_{\text{total}}} = \frac{1}{3.0 \, \mu\text{F}} + \frac{1}{6.0 \, \mu\text{F}} \] Simplifying: \[ \frac{1}{C_{\text{total}}} = \frac{1}{3} + \frac{1}{6

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Shown in the circuit below is a battery providing 12 V voltage to a circuit of capacitors. a. Find the equivalent capacitance of the combination of capacitors in the circuit. b. What charge flows through the battery as the capacitors are being charged? 3.0 μF 12 V 5.0 μF Ł 1.0 μF

Shown in the circuit below is a battery providing 12 V voltage to a circuit of capacitors. a. Find the equivalent capacitance of the combination of capacitors in the circuit. b. What charge flows through the battery as the capacitors are being charged? 3.0 μF 12 V 5.0 μF Ł 1.0 μF

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Combination of Capacitors

The connection of capacitors can be established in a circuit in two ways.

Question

### Educational Resource: Capacitor Circuits

---

#### Analysis of a Capacitor Circuit

**Problem:**

Shown in the circuit below is a battery providing 12 V voltage to a circuit of capacitors.

1. **Find the equivalent capacitance of the combination of capacitors in the circuit.**
2. **What charge flows through the battery as the capacitors are being charged?**

**Circuit Diagram:**

- The circuit contains a battery with a voltage of 12 V.
- There are three capacitors in the circuit:
- Capacitor 1: 3.0 µF
- Capacitor 2: 5.0 µF
- Capacitor 3: 1.0 µF

The capacitors are arranged as follows based on the provided circuit:
- Capacitor 1 (3.0 µF) is in series with a parallel combination of Capacitor 2 (5.0 µF) and Capacitor 3 (1.0 µF).

**Steps to Solve:**

1. **Find the equivalent capacitance of the parallel capacitors (5.0 µF and 1.0 µF):**

In parallel, capacitances add up directly:
\[
C_{\text{parallel}} = C_2 + C_3 = 5.0 \, \mu\text{F} + 1.0 \, \mu\text{F} = 6.0 \, \mu\text{F}
\]

2. **Determine the overall equivalent capacitance of the series combination:**

The capacitors are now a series combination of 3.0 µF and 6.0 µF. The formula for capacitors in series is:
\[
\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_{\text{parallel}}}
\]
Substituting the values:
\[
\frac{1}{C_{\text{total}}} = \frac{1}{3.0 \, \mu\text{F}} + \frac{1}{6.0 \, \mu\text{F}}
\]
Simplifying:
\[
\frac{1}{C_{\text{total}}} = \frac{1}{3} + \frac{1}{6

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