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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?

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?

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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.
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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