A Level Physics Notes: Electricity – Charging and Discharging Capacitors
The fundamental equation connecting capacitance, voltage and
charge is
Charge=Voltage*Capacitance (1)
If a battery is connected to a capacitor, the voltage across the
capacitor will not instantly become the battery voltage. Instead
current will flow in the circuit. Negative charge will collect on one
plate and positive charge on the other. The voltage across the
capacitor will build up and as it does the voltage available to drive
the current through the internal resistance of the battery will
decrease. Eventually after an infinite time, the voltage across the
capacitor will reach the battery voltage and no current will flow. At
each point during the charging of the capacitor equation (1) is
obeyed. We can also related the voltage across the capacitor to the
time elapsed since the battery was connected:
where
is
the emf of the battery.
But then (1) gives the charge across the capacitor at any
time
since
if we multiply both sides by
we obtain
where
is
the charge stored on the fully charged capacitor.
We can also find the current in the circuit at any time
by
differentiating
obtaining
(2)
Now
Substituting
this into (2) gives
But
is
the initial current
so
The
qualitative graphs of
and
are
shown below.
Similar arguments give the analogous equations for discharging capacitors.
and
The
qualitative graph of V,Q and I against t is shown below, indicating
exponential decay.
