In charging a
capacitor, when the switch is closed, the charge builds up on the plates
rapidly at first and then exponentially more slowly as repulsion between like
capacitor, when the switch is closed, the charge builds up on the plates
rapidly at first and then exponentially more slowly as repulsion between like
charges retards the progress. As opposite charges accumulate on the plates of
the capacitor due to the separation of charge, a voltage develops across the
capacitor due to the electric field of these charges. In this situation, work
has to be done by increasing effort against the ever increasing electric field
as more charge is separated.
The energy
stored in the capacitor which is measured in joules is equal to the amount of
work required to establish the voltage across the capacitor, and therefore the electric
field.
stored in the capacitor which is measured in joules is equal to the amount of
work required to establish the voltage across the capacitor, and therefore the electric
field.
Energy or work
done = Charge x Potential difference
done = Charge x Potential difference
W = QV
And Q = CV
Plotting a Graph of Charge against Potential
Difference
Difference
The capacitor
is charged with charge Q to a voltage V
is charged with charge Q to a voltage V
If the
capacitor is discharge by a little amount so that the potential difference drops,
δV. There is a
resulting little energy loss (δW). This can be worked out by moderating the
equation above as
capacitor is discharge by a little amount so that the potential difference drops,
δV. There is a
resulting little energy loss (δW). This can be worked out by moderating the
equation above as
ΔW =
δV x Q
δV x Q
If
the capacitor is discharge completely,
the capacitor is discharge completely,
Energy loss = Area of shaded
triangle
triangle
∆W (for a capacitor charge or discharge) = ½ QV
But Q = CV
Therefore, ∆W = ½ CV2
Or ∆W = ½ (Q2)/C
The maximum energy that an be safely stored in a capacitor is limited by
the maximum electric field that the dielectric between the parallel plates can
withstand before it breaks down. Therefore, capacitors of the same type have
the same maximum energy density (joules of energy per cubic metre).
the maximum electric field that the dielectric between the parallel plates can
withstand before it breaks down. Therefore, capacitors of the same type have
the same maximum energy density (joules of energy per cubic metre).