1. Introduction to Capacitance

2. The Capacitance (C) of a capacitor is defined as:
Capacitors
A capacitor is made up of 2 conductors carrying charges of equal magnitude and opposite sign.
The Capacitance (C) of a capacitor is defined as:
where Q is the charge on either conductor and ∆V is the potential difference between them
The SI unit of conductance is the farad (F)  1 F = 1 coulomb per volt (C/V)

3. Parallel-Plate Capacitors
Two metallic plates of equal area “A” are separated by a distance “d”. One plate carries a + charge while the other carries a – charge.
The surface density of each plate is
The electric field between the plates is

4. Parallel-Plate Capacitors
Since the field between the plates is uniform and points directly from one plate to the other, the magnitude of the potential difference between the two equals Ed
Therefore the capacitance is given by:

5. Combinations of Capacitors
Capacitors can be combined in electric circuits.
When studying circuits a circuit diagram can be used and specific circuit symbols are given to designate a capacitor, battery, and switch.
Capacitor Symbol
Battery Symbol
Switch Symbol

6. Various Combinations Parallel Combination Series Combination
∆V1=∆V2=∆V
Q total=Q1+Q2
Equivalent capacitor
Q total = Cequiv(∆V)
Cequiv = C1+C2+C3…
Series Combination
∆Vtotal=∆V1+∆V2
Q1=Q2=Q
Equivalent capacitance
1/Cequiv = 1/C1 + 1/C2 + 1/C3…

7. Energy Stored in Charged Capacitor
Electric potential energy is stored in the system
Energy stored in a charged capacitor
The energy in a capacitor is stored in the electric field between the two plates as the capacitor is charged.
The electric field is proportional to the charge on the capacitor

8. Capacitors with Dielectrics
A Dielectric is a non-conducting material like rubber or glass.
The Dielectric constant (κ) varies from from one material to the next.
The capacitance of a capacitor containing a dielectric is:
With the addition of the dielectric the charge remains the same, the potential difference decreases, and the capacitance increases.
The capacitance increases by the factor “κ” when the dielectric is filling the space between the plates.