PHYS 142 Chapter 26 Smart Notes
26.1: Definition of Capacitance
A combination of two conductors is called a capacitor. The conductors are called
plates. If the conductors carry charges of equal magnitude and opposite sign, a
potential difference exists between them.
The capacitance C of a capacitor is defined as the ratio of the magnitude
of the charge on either conductor to the magnitude of the potential
difference between the conductors
To understand capacitance, think of similar notions that use a similar
word. The capacitance of a capacitor is the amount of charge the
capacitor can store per unit of potential difference.
Capacitance is always a positive quantity.
1F (farad) = 1 C/V
26.2: Calculating Capacitance
o Capacitance of an Isolated Charged Sphere
o Parallel Plate Capacitors
As a capacitor is being charged by a battery, electrons flow into the negative
plate and out of the positive plate.
Consider the situation before any charges have had a chance to move in
response to this change. Because no charges have moved, the electric field
between the plates has the same value but extends over a shorter distance.
2 Therefore the magnitude of the potential difference between the plates is
When the potential difference between the plates again matches that of the
battery, the flow of charge stops.
26.3: Combinations of Capacitors
o In studying electric circuits, we use a simplified pictorial representation called a circuit
diagram. Such a diagram uses circuit symbols to represent various circuit elements.
o Parallel Combination of Capacitors
The individual potential differences across capacitors connected in parallel are
the same and are equal to the potential difference applied across the
Sum of the charges on the individual capacitors
Equivalent Capacitance for Capacitors in Parallel
o Series Combination
Voltage between the Two Capacitors
Equivalent Capacitance for Capacitors in Series
26.4: Energy Stored in a Charged Capacitor
o Because positive and negative charges are separated in the system of two conductors in
a capacitor, electric potential energy is stored in the system. The discharge can often be
observed as a visible spark. If you accidentally touch the opposite plates of a charged
capacitor, your fingers act as a pathway for discharge and the result is an electric shock.
The degree of shock you receive depends on the capacitance and the voltage applied to
4 Note: Work must be done to move additional charge through the potential
difference between plates.
When the switch is closed
The battery establishes an electric field in the wires and charges flow
between the wires and capacitor.
Some of the chemical energy in the battery is converted to electric
potential energy associated with the separation of positive and negative
charges on the plate.