Capacitor
Parallel Plates
 Charged plates each store
+
-
charge.
• Positive charge at higher
potential
• Negative charge at lower
potential
 The charge storing device is
called a capacitor.
• Old term condenser
+
-
Capacitance
 The measure of a device to store charge at a given
voltage is its capacitance.
Q
C
V
 The unit of capacitance is the farad (F).
• 1F=1C/V
• Farads are a large amount of capacitance
• Microfarads (mF) and picofarads (pF) are common
Isolated Charge
 A metal sphere with a 0.25 m
radius is in a vacuum. Find the
capacitance.
 Note there is only one surface,
but the formula still works.
 The potential of the sphere is
V
kQ
Q

r
40 r
 The capacitance is
C
Q
r
 40 r 
V
k
 For the sphere
• C=
(0.25 m) / (8.99 x 109 Nm2/C2)
• C = 28 x 10-12 F = 28 pF.
Parallel Plate Capacitor
+
 A capacitor is made from two
-
plates.
• Area A
• Distance d
 The field is due to the charge
on the plates
• E = Q/A
+
 The voltage is V = Ed.
 The capacitance is
C
Q Q
Q


V Ed Qd A
C
A
d
-
Keyboarding
 A key on a keyboard is a
parallel plate capacitor.
 A springy insulator separates
the plates.
 A circuit measures the
capacitance from each key.
• If pressed d decreases
• The capacitance increases
• The circuit records the key
Two Capacitors
Q  C1V + C2V
 Two capacitor charged by the
C1
+
-
same potential are in parallel.
Q1  C1V
 The voltage is the same across
each capacitor.
 The charge will be equal to the
total from both.
C2
Q2  C2V
 The total capacitance is the
sum of the individual
capacitances.
+
-
C
Q C1V + C2V

V
V
C  C1 + C2
Series Capacitors
 Two capacitors connected is
Q  Q1  Q2
Q1  C1V
+
Q2  C2V
-
sequence with the ends
separated by a potential are in
series.
 The total charge on the middle
section must be neutral.
• Same charge on capacitors
• Voltages sum to the total
C1
+
C2
-
C
Q
Q
1


V1 + V2 Q / C1 + Q / C2 1 / C1 + 1 / C2
1
1
1

+
C C1 C2
More and Less
 Two capacitors 1mF and 3 mF
are placed in parallel and in
series.
 Find the combined
capacitance in both situations.
 In parallel the capacitances
add directly.
 In series the inverses are
summed, then inverted.
1
1
1

+
C C1 C2
 1 (μF)-1 + 1/3 (μF)-1 = 4/3 (μF)-1
 C = 3/4 μF
C  C1 + C2
 C = 1 μF + 3 μF = 4 μF
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