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Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C, = 3C, C, = C, and C3 = 5C. |C3 (a) What is the equivalent capacitance of this set of capacitors (in terms of C)? Ceq (b) State the ranking of the capacitors according to the charge they store, from largest to smallest. Q > Q

Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C, = 3C, C, = C, and C3 = 5C. |C3 (a) What is the equivalent capacitance of this set of capacitors (in terms of C)? Ceq (b) State the ranking of the capacitors according to the charge they store, from largest to smallest. Q > Q

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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### Educational Content on Capacitors In this exercise, we examine a circuit with three capacitors connected to a battery, as illustrated in the diagram. The capacitors have the following capacitances: - Capacitor \( C_1 = 3C \) - Capacitor \( C_2 = C \) - Capacitor \( C_3 = 5C \) **Figure Explanation:** The circuit diagram shows the three capacitors in a combination of series and parallel connections: - \( C_2 \) is in parallel with \( C_3 \). - The parallel combination of \( C_2 \) and \( C_3 \) is in series with \( C_1 \). **Tasks:** (a) **Calculate the Equivalent Capacitance:** Determine the equivalent capacitance (\( C_{eq} \)) of the set of capacitors in terms of \( C \). \[ C_{eq} = \, \_\_\_\_ \] (b) **Rank the Capacitors by Stored Charge:** Rank the capacitors from largest to smallest based on the charge they store. \[ Q_{\, \_\_\_} > Q_{\, \_\_\_} > Q_{\, \_\_\_} \] (c) **Rank the Capacitors by Potential Difference:** Rank the capacitors from largest to smallest based on the potential differences across them. - \( \Delta V_1 > \Delta V_2 = \Delta V_3 \) - \( \Delta V_1 = \Delta V_2 < \Delta V_3 \) - \( \Delta V_2 > \Delta V_3 > \Delta V_1 \) - \( \Delta V_1 > \Delta V_2 > \Delta V_3 \) This exercise helps in understanding the concepts of capacitive combinations, charge distribution in capacitors, and potential differences across them.
Transcribed Image Text:### Educational Content on Capacitors In this exercise, we examine a circuit with three capacitors connected to a battery, as illustrated in the diagram. The capacitors have the following capacitances: - Capacitor \( C_1 = 3C \) - Capacitor \( C_2 = C \) - Capacitor \( C_3 = 5C \) **Figure Explanation:** The circuit diagram shows the three capacitors in a combination of series and parallel connections: - \( C_2 \) is in parallel with \( C_3 \). - The parallel combination of \( C_2 \) and \( C_3 \) is in series with \( C_1 \). **Tasks:** (a) **Calculate the Equivalent Capacitance:** Determine the equivalent capacitance (\( C_{eq} \)) of the set of capacitors in terms of \( C \). \[ C_{eq} = \, \_\_\_\_ \] (b) **Rank the Capacitors by Stored Charge:** Rank the capacitors from largest to smallest based on the charge they store. \[ Q_{\, \_\_\_} > Q_{\, \_\_\_} > Q_{\, \_\_\_} \] (c) **Rank the Capacitors by Potential Difference:** Rank the capacitors from largest to smallest based on the potential differences across them. - \( \Delta V_1 > \Delta V_2 = \Delta V_3 \) - \( \Delta V_1 = \Delta V_2 < \Delta V_3 \) - \( \Delta V_2 > \Delta V_3 > \Delta V_1 \) - \( \Delta V_1 > \Delta V_2 > \Delta V_3 \) This exercise helps in understanding the concepts of capacitive combinations, charge distribution in capacitors, and potential differences across them.
(d) Assume \( C_3 \) is increased. Explain what happens to the charge stored by each capacitor. - \( Q_3 \), \( Q_1 \), and \( Q_2 \) increase. - \( Q_3 \) and \( Q_2 \) increase; \( Q_1 \) decreases. - All charges stay the same. - \( Q_3 \) and \( Q_1 \) increase; \( Q_2 \) decreases.
Transcribed Image Text:(d) Assume \( C_3 \) is increased. Explain what happens to the charge stored by each capacitor. - \( Q_3 \), \( Q_1 \), and \( Q_2 \) increase. - \( Q_3 \) and \( Q_2 \) increase; \( Q_1 \) decreases. - All charges stay the same. - \( Q_3 \) and \( Q_1 \) increase; \( Q_2 \) decreases.
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