What is a true statement about the capacitors connected in series illustrated below? C 30 AV O The energy stored in the capacitor of capacitance 3C is nine times larger than the energy stored in the capacitor of capacitance C O The energy stored in each capacitor is the same. O The energy stored in the capacitor of capacitance 3C is three times larger than the energy stored in the capacitor of capacitance C. O The energy stored in the capacitor of capacitance 3C is three times smaller than the energy stored in the capacitor of capacitance C. O The energy stored in the capacitor of capacitance 3C is nine times smaller than the energy stored in the capacitor of capacitance C.
What is a true statement about the capacitors connected in series illustrated below? C 30 AV O The energy stored in the capacitor of capacitance 3C is nine times larger than the energy stored in the capacitor of capacitance C O The energy stored in each capacitor is the same. O The energy stored in the capacitor of capacitance 3C is three times larger than the energy stored in the capacitor of capacitance C. O The energy stored in the capacitor of capacitance 3C is three times smaller than the energy stored in the capacitor of capacitance C. O The energy stored in the capacitor of capacitance 3C is nine times smaller than the energy stored in the capacitor of capacitance C.
Introductory Circuit Analysis (13th Edition)
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![### Capacitors in Series: Understanding Energy Storage
#### Problem Statement:
What is a true statement about the capacitors connected in series illustrated below?
#### Diagram Explanation:
The diagram shows two capacitors connected in series:
- The first capacitor has capacitance \( C \).
- The second capacitor has capacitance \( 3C \).
- The total voltage across the series combination is \( \Delta V \).
```
C 3C
+ | |-----| | |
|
+V
```
#### Choices:
- (A) The energy stored in the capacitor of capacitance \( 3C \) is nine times larger than the energy stored in the capacitor of capacitance \( C \).
- (B) The energy stored in each capacitor is the same.
- (C) The energy stored in the capacitor of capacitance \( 3C \) is three times larger than the energy stored in the capacitor of capacitance \( C \).
- (D) The energy stored in the capacitor of capacitance \( 3C \) is three times smaller than the energy stored in the capacitor of capacitance \( C \).
- (E) The energy stored in the capacitor of capacitance \( 3C \) is nine times smaller than the energy stored in the capacitor of capacitance \( C \).
In capacitors connected in series, the charge \( Q \) on each capacitor is the same. The energy stored in a capacitor \( E \) can be expressed as:
\[ E = \frac{Q^2}{2C} \]
Given that both capacitors have the same charge:
- Energy stored in capacitor \( C \):
\[ E_C = \frac{Q^2}{2C} \]
- Energy stored in capacitor \( 3C \):
\[ E_{3C} = \frac{Q^2}{6C} \]
Thus, the energy stored in the capacitor of capacitance \( 3C \) is one-third of the energy stored in the capacitor of capacitance \( C \).
Given this analysis, the correct answer is:
- (D) The energy stored in the capacitor of capacitance \( 3C \) is three times smaller than the energy stored in the capacitor of capacitance \( C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a5ac3c6-e4ab-423a-91e1-ff33bdae0d07%2F339df24b-e51c-4262-91bf-61708c836672%2Fv0250a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Capacitors in Series: Understanding Energy Storage
#### Problem Statement:
What is a true statement about the capacitors connected in series illustrated below?
#### Diagram Explanation:
The diagram shows two capacitors connected in series:
- The first capacitor has capacitance \( C \).
- The second capacitor has capacitance \( 3C \).
- The total voltage across the series combination is \( \Delta V \).
```
C 3C
+ | |-----| | |
|
+V
```
#### Choices:
- (A) The energy stored in the capacitor of capacitance \( 3C \) is nine times larger than the energy stored in the capacitor of capacitance \( C \).
- (B) The energy stored in each capacitor is the same.
- (C) The energy stored in the capacitor of capacitance \( 3C \) is three times larger than the energy stored in the capacitor of capacitance \( C \).
- (D) The energy stored in the capacitor of capacitance \( 3C \) is three times smaller than the energy stored in the capacitor of capacitance \( C \).
- (E) The energy stored in the capacitor of capacitance \( 3C \) is nine times smaller than the energy stored in the capacitor of capacitance \( C \).
In capacitors connected in series, the charge \( Q \) on each capacitor is the same. The energy stored in a capacitor \( E \) can be expressed as:
\[ E = \frac{Q^2}{2C} \]
Given that both capacitors have the same charge:
- Energy stored in capacitor \( C \):
\[ E_C = \frac{Q^2}{2C} \]
- Energy stored in capacitor \( 3C \):
\[ E_{3C} = \frac{Q^2}{6C} \]
Thus, the energy stored in the capacitor of capacitance \( 3C \) is one-third of the energy stored in the capacitor of capacitance \( C \).
Given this analysis, the correct answer is:
- (D) The energy stored in the capacitor of capacitance \( 3C \) is three times smaller than the energy stored in the capacitor of capacitance \( C \).
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