AP Physics C: Electricity and Magnetism
Advanced Placement Physics C: Electricity and Magnetism with calculus applications.
Capacitance and Dielectrics
What is Capacitance?
Capacitance measures a system’s ability to store electric charge. It’s defined as the ratio of charge to voltage:
\[ C = \frac{Q}{V} \]
Parallel Plate Capacitors
For two parallel plates,
\[ C = \varepsilon_0 \frac{A}{d} \] where \( A \) is plate area and \( d \) is the distance between them.
Dielectrics
Inserting a dielectric material between the plates increases capacitance by reducing the electric field, allowing more charge storage for the same voltage.
Calculus Connection
When voltage or charge changes with time, calculus helps us analyze how energy is stored and released.
Real-World Application
Capacitors are everywhere in electronics, from camera flashes to tuning circuits!
Key Formula
\[C = \varepsilon_0 \frac{A}{d}\]
Examples
Calculating the capacitance of a capacitor filled with glass.
Determining energy stored in a defibrillator’s capacitor.
In a Nutshell
Capacitance measures how much electric charge can be stored, and dielectrics boost this ability.