### Example Problem 9: Series RC Circuit AnalysisA series RC circuit consists of a 40 µF capacitor, a 6.0 Ω resistor, and a 24 V voltage source. With the capacitor initially uncharged, an open switch in the circuit is closed at time \( t = 0 \) s.**a.** At the instant that the switch is closed, what is the voltage across the resistor, the voltage across the capacitor, and the current flowing through the circuit? *(Answers: 24 V, 0 V, 4.0 A)***b.** After the switch has been closed for four time constants, what is the voltage across and the charge on the capacitor? *(Answers: 23.56 V, 942 µC)*#### Explanation:- When the switch is first closed, the voltage across the capacitor is initially 0 V since it is uncharged. The entire voltage of 24 V from the voltage source appears across the resistor, resulting in an initial current \( I = \frac{V}{R} = \frac{24V}{6\Omega} = 4.0 \) A. - After a long time (specifically after four time constants), we can calculate the voltage across the capacitor and the charge on it by considering the time constant \( \tau = RC \). The voltage across the capacitor \( V_c \) will approach the voltage source of 24 V, but practically will be slightly less, approximately 23.56 V after four time constants. The charge \( Q \) on the capacitor can be found using \( Q = C \cdot V_c = 40 \mu F \cdot 23.56 V = 942 \mu C \).For educational purposes, students should refer to additional RC circuit formulas and characteristics found in their physics or electrical engineering textbooks.

Answered: Image /qna-images/answer/2e17eaeb-4592-4789-83bb-560af932f3fe.jpg

9. A series RC circuit consists of a 40 µF capacitor, a 6.0 Q resistor, and a 24 V voltage source. With the capacitor initially uncharged, an open switch in the circuit is closed at time t = 0 s. a. At the instant that the switch is closed, what is the voltage across the resistor, the voltage across the capacitor, and the current flowing through the circuit? (24 V, OV, 4.0 A) b. After the switch has been closed for four time constants, what is the voltage across and the charge on the capacitor? (23 56 V 942 UC)

9. A series RC circuit consists of a 40 µF capacitor, a 6.0 Q resistor, and a 24 V voltage source. With the capacitor initially uncharged, an open switch in the circuit is closed at time t = 0 s. a. At the instant that the switch is closed, what is the voltage across the resistor, the voltage across the capacitor, and the current flowing through the circuit? (24 V, OV, 4.0 A) b. After the switch has been closed for four time constants, what is the voltage across and the charge on the capacitor? (23 56 V 942 UC)

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Example Problem 9: Series RC Circuit Analysis

A series RC circuit consists of a 40 µF capacitor, a 6.0 Ω resistor, and a 24 V voltage source. With the capacitor initially uncharged, an open switch in the circuit is closed at time \( t = 0 \) s.

**a.** At the instant that the switch is closed, what is the voltage across the resistor, the voltage across the capacitor, and the current flowing through the circuit? *(Answers: 24 V, 0 V, 4.0 A)*

**b.** After the switch has been closed for four time constants, what is the voltage across and the charge on the capacitor? *(Answers: 23.56 V, 942 µC)*

#### Explanation:

- When the switch is first closed, the voltage across the capacitor is initially 0 V since it is uncharged. The entire voltage of 24 V from the voltage source appears across the resistor, resulting in an initial current \( I = \frac{V}{R} = \frac{24V}{6\Omega} = 4.0 \) A.

- After a long time (specifically after four time constants), we can calculate the voltage across the capacitor and the charge on it by considering the time constant \( \tau = RC \). The voltage across the capacitor \( V_c \) will approach the voltage source of 24 V, but practically will be slightly less, approximately 23.56 V after four time constants. The charge \( Q \) on the capacitor can be found using \( Q = C \cdot V_c = 40 \mu F \cdot 23.56 V = 942 \mu C \).

For educational purposes, students should refer to additional RC circuit formulas and characteristics found in their physics or electrical engineering textbooks.

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