Capacitors in Circuits Q A V E d +Q Capacitance Two parallel plates charged Q and –Q respectively constitute a capacitor C = Q / V The relationship C = Q / V is valid for any charge configuration (Indeed this is the definition of capacitance or electric capacity)
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A
V
E
d
+Q
CapacitanceTwo parallel plates charged
Q and –Q respectively
constitute a capacitor
C = Q / V
The relationship C = Q / V is valid for any charge configuration
(Indeed this is the definition of capacitance or electric capacity)
In the particular case of a parallel plate capacitor
C = 0 A / d [vacuum] or C = 0 A / d [dielectric]
The capacitance is directly proportional to the area of the plates
and inversely proportional to the separation between the plates
(Symbol for
a capacitor)
+Q
Q
C
V
A piece of metal in equilibrium has a constant value of potential.
Thus, the potential of a plate and attached wire is the same.
The potential difference between the ends of the wires is V,
the same as the potential difference between the plates.
C1  q1
a
b
C2  q2
V
b
a
C  q
C = C1 + C2
C1
C2
C
a
q
+q
q
+q
b
a
q
+q
b
V1
V2
V
1 / C = 1 / C1 + 1 / C2
Ideal circuit
What happens when
the switch is closed ?
How does the capacitor acquire the charge ?
closed
I
R
R
VR=IR
+
+
+++
V
V
  
VC=q/C

C

C
V = I(t)R + q(t)/C
When the switch closes, at first a high current flows:
VR is big and VC is small. As q is stored in C, VC increases.
This fights against the battery, so I gradually decreases.
Finally, I stops (I = 0), C is fully charged (VC = Q/C = V),
and Q=C V
R
VR=IR
+q
+q
I
C
VC=V0
C
q
VC=q/C
q
Open circuit
After closing switch
Current will flow through the resistor for a while.
Eventually, the capacitor will lose all its charge,
and the current will go to zero.
During the transient: q(t) / C – I(t) R = 0
Charging and Discharging a Capacitor
Charging and discharging of a capacitor occurs gradually
with a characteristic time = RC time constant
At t = 0, (switch closed or open) a large current flows,
the capacitor behaves like a short circuit.
At t , the current is essentially zero,
the capacitor behaves like an open switch.
The current decreases exponentially.
Current and Voltage
in a circuit
The ammeter measures current,
and is connected in series.
The voltmeter measures voltage,
and is connected in parallel.
A modern digital multimeter combines the functions
of ammeter, voltmeter, and ohmmeter.
(i.e. can measure current, voltage, and resistance)
In addition, modern multimeters can measure
capacitance, temperature, and more,
and can be connected to computers too…