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How much energy is stored in the capacitor?
Had the capacitor been connected to a 6.00-V battery, how much energy would have been stored?
![### Capacitor Energy Storage
#### Problem Statement
(a) A 4.00-μF capacitor is connected to a 9.00-V battery. How much energy is stored in the capacitor?
- [Answer: _______ μJ]
(b) Had the capacitor been connected to a 6.00-V battery, how much energy would have been stored?
- [Answer: _______ μJ]
#### Explanation
**Capacitor and Battery Connection:**
- A **capacitor** is an electrical component that stores energy in an electric field. Its ability to store charge is measured in **farads (F)**.
- The energy (E) stored in a capacitor with a capacitance (C) and a voltage (V) applied is given by the formula:
\[
E = \frac{1}{2} C V^2
\]
Here, the energy is measured in joules (J), but often converted to microjoules (μJ) for convenience in small-scale circuits.
**Given Values:**
1. Capacitance, \( C = 4.00 \, \mu F \)
2. Voltage cases:
- \( V_1 = 9.00 \, V \)
- \( V_2 = 6.00 \, V \)
**Tasks:**
- Calculate the stored energy in microjoules (μJ) for each voltage case.
Utilize the formula mentioned above for both scenarios to determine the energy stored in the capacitor.](https://content.bartleby.com/qna-images/question/f90dea9d-9cdb-42ca-abaa-dad0efc4d5b4/10fed8f3-ee94-4412-91fb-38d9af7eb0cf/u7fzws_processed.jpeg)
Transcribed Image Text:### Capacitor Energy Storage
#### Problem Statement
(a) A 4.00-μF capacitor is connected to a 9.00-V battery. How much energy is stored in the capacitor?
- [Answer: _______ μJ]
(b) Had the capacitor been connected to a 6.00-V battery, how much energy would have been stored?
- [Answer: _______ μJ]
#### Explanation
**Capacitor and Battery Connection:**
- A **capacitor** is an electrical component that stores energy in an electric field. Its ability to store charge is measured in **farads (F)**.
- The energy (E) stored in a capacitor with a capacitance (C) and a voltage (V) applied is given by the formula:
\[
E = \frac{1}{2} C V^2
\]
Here, the energy is measured in joules (J), but often converted to microjoules (μJ) for convenience in small-scale circuits.
**Given Values:**
1. Capacitance, \( C = 4.00 \, \mu F \)
2. Voltage cases:
- \( V_1 = 9.00 \, V \)
- \( V_2 = 6.00 \, V \)
**Tasks:**
- Calculate the stored energy in microjoules (μJ) for each voltage case.
Utilize the formula mentioned above for both scenarios to determine the energy stored in the capacitor.
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