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Two capacitors, C 1 = 18.0 μ F and C 2 = 36.0 μ F, are connected in series, and a 12.0-V battery is connected across the two capacitors. Find (a) the equivalent capacitance and (b) the energy stored in this equivalent capacitance. (c) Find the energy stored in each individual capacitor. (d) Show that the sum of these two energies is the same as the energy found in part (b). (e) Will this equality always be true, or docs it depend on the number of capacitors and their capacitances? (f) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)? (g) Which capacitor stores more energy in this situation, C 1 or C 2 ?

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Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

Solutions

Chapter
Section
BuyFindarrow_forward

Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 25, Problem 18P
Textbook Problem
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Two capacitors, C1 = 18.0 μF and C2 = 36.0 μF, are connected in series, and a 12.0-V battery is connected across the two capacitors. Find (a) the equivalent capacitance and (b) the energy stored in this equivalent capacitance. (c) Find the energy stored in each individual capacitor. (d) Show that the sum of these two energies is the same as the energy found in part (b). (e) Will this equality always be true, or docs it depend on the number of capacitors and their capacitances? (f) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)? (g) Which capacitor stores more energy in this situation, C1 or C2?

(a)

To determine
The equivalent capacitance of the system.

Explanation of Solution

Given information: The value of capacitor 1 is 18.0μF , value of capacitor 2 is 36.0μF , voltage of the battery is 12.0V .

Explanation:

The capacitors C1andC2 are in series.

Formula to calculate the equivalent capacitance of the system when they are connected in series.

1Ceq=1C1+1C2 (1)

Here,

Ceq is the equivalent capacitance of the system when they are connected in series.

C1 is the value of capacitor 1.

C2 is the value of capacitor 2

(b)

To determine
The energy stored in this equivalent capacitance.

(c)

To determine
The energy stored in each individual capacitor.

(d)

To determine

To show: The sum of these two energies is the same as the energy found in part (b).

(e)

To determine
The reason that this equality will always be true, or the reason that it depends on the number of capacitors and their capacitances.

(f)

To determine
The required potential difference across them so that the combination stores the same energy as in part (b).

(g)

To determine
The capacitor stores more energy C1orC2 .

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Chapter 25 Solutions

Physics for Scientists and Engineers
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