Overview
This lecture explains how capacitors store and release electric potential energy, the relationship to capacitance and voltage, and how these principles are used in devices like defibrillators.
Defibrillators and Capacitors
- A defibrillator delivers a jolt of electricity to restore a normal heartbeat by discharging a capacitor.
- A capacitor stores electric potential energy and releases it quickly as current.
Capacitors: Structure and Function
- A capacitor consists of two parallel conductive plates with opposite charges, separated by an electric field.
- Energy is stored as electric potential energy in the field between the plates.
- The amount of potential energy depends on the strength of the electric field and the amount of stored charge.
Electric Potential and Voltage
- Electric potential energy is analogous to gravitational potential energy.
- Work is done when a charge moves between capacitor plates due to the electric field.
- Voltage (electric potential difference) is defined as the change in potential energy per unit charge.
- Voltage across a capacitor equals the negative electric field times the distance between plates.
Calculating Fields and Potentials
- Electric field (E) between capacitor plates is force divided by charge, or voltage divided by distance.
- Equipotential lines, which represent equal voltage, are parallel to capacitor plates and perpendicular to the electric field.
Point Charges and Electric Potential
- Electric potential for a point charge is found by integrating the electric field from infinity to a point near the charge.
- Equipotential lines around point charges are circular; for dipoles, patterns are more complex due to two charges.
Capacitance and Dielectrics
- Capacitance is the amount of charge stored per unit voltage, measured in Farads (Coulombs/Volt).
- Capacitance increases with plate area and decreases with plate separation.
- Inserting a dielectric (insulator) increases capacitance by allowing plates to get closer and aligning with the field to weaken it.
- The dielectric constant (K) quantifies this effect.
Energy Storage in Capacitors
- Energy stored in a capacitor: ( U = \frac{1}{2} QV ) (charge times voltage divided by two).
- Energy density in the electric field: ( \text{Energy density} = \frac{1}{2} \epsilon_0 E^2 ) (epsilon naught times electric field squared divided by two).
Key Terms & Definitions
- Capacitor — Device with two plates that stores electric charge and energy.
- Electric Potential Energy — Energy a charge has due to its position in an electric field.
- Voltage (Electric Potential Difference) — Potential energy per unit charge; measured in Volts.
- Capacitance — Amount of charge a capacitor can store per unit voltage; measured in Farads.
- Dielectric — Insulating material increasing a capacitor's capacitance by preventing charge leakage.
- Equipotential Lines — Lines where electric potential (voltage) is equal.
- Electric Field (E) — Force per unit charge between plates or around charges.
Action Items / Next Steps
- Review formulas for electric potential, capacitance, and energy density.
- Practice calculating voltage, capacitance, and stored energy for different capacitor configurations.