(a) A 3.00-μF capacitor is connected to a 12.0-V battery. How much energy is stored in the capac

step 1 So we have a capacitor with 3 micro -farrid capacitance, and that's connected to a 12 -volt batt

(a) A 3.00-μF capacitor is connected to a 12.0-V battery....

(a) A $3.00-\mu \mathrm{F}$ capacitor is connected to a $12.0-\mathrm{V}$ battery. How much energy is stored in the capacitor? (b) If the capacitor had been connected to a $6.00-\mathrm{V}$ battery, how much energy would have been stored?

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Key Concepts

Energy Storage in Capacitors

The energy stored in a capacitor is given by the formula U = ½ CV², where U is the energy, C is the capacitance, and V is the applied voltage. This relationship shows that the stored energy not only depends on the capacitance but also increases with the square of the voltage, making the voltage level critically important in energy storage applications.

Voltage

Voltage is the electrical potential difference across the capacitor's plates and is the driving force that moves charge into the capacitor. In the context of energy storage, voltage directly affects the amount of energy stored since even small changes in voltage can lead to significant differences in the stored energy due to its quadratic relationship in the energy formula.

Capacitance

Capacitance is a fundamental property of a capacitor that measures its ability to store charge per unit voltage. It is expressed in farads and indicates how much electric charge a capacitor can hold when a potential difference is applied. This concept is central to understanding the behavior of capacitive devices in circuits.

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