Transcript Capacitor
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
40 r
The capacitance is
C
Q
r
40 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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