Unit 3: Capacitance

Big Ideas:
1. Capacitors store energy in an electric field.
2. Capacitance is determined by geometrical measurements.
3. Dielectric materials increase capacitance.

Learner Objectives (as published by the College Board):
1. Students should understand the definition and function of capacitance, so they can:
A. Relate stored charge and voltage for a capacitor.
B. Relate voltage, charge, and stored energy for a capacitor.
C. Recognize situations in which energy stored in a capacitor is converted to other forms.

2. Students should understand the physics of the parallel-plate capacitor, so they can:
A. Describe the electric field inside the capacitor, and relate the strength of this field to the potential difference between the plates and the plate separation.
B. Relate the electric field to the density of the charge on the plates.
C. Derive an expression for the capacitance of a parallel-plate capacitor.
D. Determine how changes in dimension will affect the value of the capacitance.
E. Derive and apply expressions for the energy stored in a parallel-plate capacitor and for the energy density in the field between the plates.
F. Analyze situations in which capacitor plates are moved apart or moved closer together, or in which a conducting slab is inserted between capacitor plates, either with a battery connected between the plates or with the charge on the plates held fixed.

3. Students should understand cylindrical and spherical capacitors, so they can:
A. Describe the electric field inside each.
B. Derive an expression for the capacitance of each.

4. Students should understand the behavior of dielectrics, so they can:
A. Describe how the insertion of a dielectric between the plates of a charged parallel-plate capacitor affects its capacitance and the field strength and voltage between the plates.
B. Analyze situations in which a dielectric slab is inserted between the plates of a capacitor.