Energy of a capacitor | Circuits | Physics | Khan Academy

TL;DR

Capacitors store energy and release it when connected to a circuit, with the energy formula being 1/2 the charge times the voltage.

Transcript

SPEAKER 1: Check out this capacitor. Look at what happens if I hook it up to this light bulb. CHILDREN (IN UNISON): Boo! SPEAKER 1: Yeah, nothing happened because the capacitor is not charged up. But if we look at up to a battery first, to charge up the capacitor, and then hook it up to the light bulb, the light bulb lights up. CHILDREN (IN UNISON)... Read More

Key Insights

• 🈂️ Capacitors store both charge and energy when charged up.
• 🙂 Energy stored in a capacitor is released as light and heat when connected to a circuit.
• 💦 The energy formula for capacitors includes a 1/2 factor because charges drop through decreasing voltages during discharge.
• ❓ There are two alternative formulas for calculating capacitor energy, depending on the known variables.
• ⚡ The voltage in the energy formula refers to the voltage across the capacitor, not necessarily the battery voltage.

Questions & Answers

Q: How does a capacitor store energy?

When a capacitor is connected to a battery, charges get separated, creating electrical potential energy stored in the capacitor.

Q: Why does the energy formula for capacitors include a 1/2 factor?

During discharge, only the first charge that gets transferred drops through the full voltage. Subsequent charges drop through decreasing voltages, resulting in the 1/2 factor in the formula.

Q: Can the energy formula for capacitors be written differently?

Yes, it can also be expressed as 1/2 times the capacitance times the voltage squared. The choice of formula depends on whether or not the charge is known.

Q: How does the voltage in the energy formula relate to the battery voltage?

In the case of a single battery charging up a single capacitor, the voltage across the capacitor is equal to the voltage of the battery. But in circuits with multiple capacitors, the voltage across a specific capacitor must be used.

Summary & Key Takeaways

• Capacitors that are charged up store electrical potential energy, which can be converted into light and heat when connected to a circuit.

• The energy of a capacitor is 1/2 the product of the charge and voltage, not just the product.

• During discharge, the charges dropped through decreasing voltages, leading to the inclusion of the 1/2 factor in the energy formula.