**Problem 1: Capacitors in a Circuit**In the figure below, a 21 V battery is connected across capacitors of the following capacitances:- \( C_1 = C_6 = 5.0 \, \mu\text{F} \)- \( C_3 = C_5 = 2.0 \, \mu\text{F} \)- \( C_2 = 6.0 \, \mu\text{F} \)- \( C_4 = 6.0 \, \mu\text{F} \)**Question:**- (a) What is the equivalent capacitance \( C_{\text{eq}} \) of the capacitors?- (b) What is the voltage \( V_3 \) across capacitor \( C_3 \)?- (c) What is the charge \( q_3 \) on capacitor \( C_3 \)?**Diagram:**The diagram features a circuit configuration where several capacitors are connected in both series and parallel arrangements to a \( 21 \, \text{V} \) battery. The arrangement of the capacitors is as follows:- \( C_1 \) and \( C_6 \) are connected in series.- \( C_4 \) is connected in parallel with the series combination of \( C_1 \) and \( C_6 \).- \( C_5 \) and \( C_3 \) are connected in series.- \( C_2 \) is connected in parallel with the series combination of \( C_5 \) and \( C_3 \).To solve the problem:1. Start by calculating the equivalent capacitance of the series and parallel combinations of capacitors.2. Use the principles of series and parallel capacitors to find the overall equivalent capacitance \( C_{\text{eq}} \).3. Determine the voltage across individual capacitors in the series configuration.4. Calculate the charge on specific capacitors using the relationship \( q = C \times V \).By following these steps, you can find the required equivalent capacitance, voltage, and charge for the specified capacitors in the circuit.

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1. In the figure a 21 V battery is connected across capacitors of capacitances C1 = C6 5.0 µF and C3 = Cs = 2.0C2 = 2.0C4 = 6.0 µF. What are (a) the equivalent capacitance Ceq of the capacitors and (b) V3 and (c) q3 of capacitor 3? %3D %3D

1. In the figure a 21 V battery is connected across capacitors of capacitances C1 = C6 5.0 µF and C3 = Cs = 2.0C2 = 2.0C4 = 6.0 µF. What are (a) the equivalent capacitance Ceq of the capacitors and (b) V3 and (c) q3 of capacitor 3? %3D %3D

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Question

**Problem 1: Capacitors in a Circuit**

In the figure below, a 21 V battery is connected across capacitors of the following capacitances:
- \( C_1 = C_6 = 5.0 \, \mu\text{F} \)
- \( C_3 = C_5 = 2.0 \, \mu\text{F} \)
- \( C_2 = 6.0 \, \mu\text{F} \)
- \( C_4 = 6.0 \, \mu\text{F} \)

**Question:**
- (a) What is the equivalent capacitance \( C_{\text{eq}} \) of the capacitors?
- (b) What is the voltage \( V_3 \) across capacitor \( C_3 \)?
- (c) What is the charge \( q_3 \) on capacitor \( C_3 \)?

**Diagram:**

The diagram features a circuit configuration where several capacitors are connected in both series and parallel arrangements to a \( 21 \, \text{V} \) battery. The arrangement of the capacitors is as follows:
- \( C_1 \) and \( C_6 \) are connected in series.
- \( C_4 \) is connected in parallel with the series combination of \( C_1 \) and \( C_6 \).
- \( C_5 \) and \( C_3 \) are connected in series.
- \( C_2 \) is connected in parallel with the series combination of \( C_5 \) and \( C_3 \).

To solve the problem:

1. Start by calculating the equivalent capacitance of the series and parallel combinations of capacitors.
2. Use the principles of series and parallel capacitors to find the overall equivalent capacitance \( C_{\text{eq}} \).
3. Determine the voltage across individual capacitors in the series configuration.
4. Calculate the charge on specific capacitors using the relationship \( q = C \times V \).

By following these steps, you can find the required equivalent capacitance, voltage, and charge for the specified capacitors in the circuit.

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