Lesson 10
CAPACITORS IN SERIES AND
PARALLEL
Lesson 10: Capacitors in Series and Parallel
AP Physics B Objectives
III.C.3. Capacitors in circuits
a) Students should understand the and steady-state behavior
of capacitors connected in series or in parallel, so they can:
(1) Calculate the equivalent capacitance of a series or parallel combination.
(2) Describe how stored charge is divided between capacitors connected in
parallel.
(3) Determine the ratio of voltages for capacitors connected in series.
(4) Calculate the voltage or stored charge, under steady-state conditions,
for a capacitor connected to a circuit consisting of a battery and resistors.
Student Objectives
Students will be able to:
1. Calculate the equivalent capacitance of series and parallel
combinations of capacitors.
2. Describe qualitatively the charging and discharging of capacitors.
Review of Capacitors
C = o A / d
capacitance of a capacitor
q = C ΔV
charge stored on a capacitor
Uc = ½ C ΔV2
energy stored in a capacitor
Capacitors in Parallel
Ceq   Ci
Derive the relationship for capacitors in
parallel from first principles.
Hint:
= V1 = V2 = V3
Sample Problem 10.1
What is the equivalent capacitance of the circuit below?
6V
2 μF
4 μF
Capacitors in Series
1
1

Ceq
Ci
Derive the relationship for capacitors in series
from first principles.
Hint:
= V1 + V2 + V3
Sample Problem 10.2
What is the equivalent capacitance of the circuit below?
C1 = 2 μF
6V
C2 = 4 μF
Comparisons
Resistors
Series
Parallel
Capacitors
Charging an RC Circuit
Discharging the Capacitor in an RC Circuit