As soon as the connection is made charge flows from the battery
terminals, along the wire and onto the plates, positive charge on
one plate, negative charge on the other.
Why? The likesign charges
on each terminal want to get away from each other. In addition to
that repulsion, there is an attraction to the oppositesign charge
on the other nearby plate. Initially the current is large, because
in a sense the charges can not tell immediately that the wire does
not really go anywhere, that there is no complete circuit of wire.
The initial current is limited by the resistance of the wires, or
perhaps by a real resistor. But as charge builds up on the plates,
charge repulsion resists the flow of more charge and the current is
reduced. Eventually, the repulsive force from charge on the plate is
strong enough to balance the force from charge on the battery
terminal, and all current stops.
Fig  2 :
The time
dependence of the current in the circuit
The existence of the separated charges on the plates means there
must be a voltage between the plates, and this voltage be equal to
the battery voltage when all current stops. After all, since the
points are connected by conductors, they should have the same
voltage; even if there is a resistor in the circuit, there is no
voltage across the resistor if the current is zero, according to
Ohm's law.
The amount of charge that collects on the plates to
produce the voltage is a measure of the value of the capacitor, its
capacitance, measured in farads (f). The relationship is C = Q/V ,
where Q is the charge in Coulombs.
Large capacitors have plates with
a large area to hold lots of charge, separated by a small distance,
which implies a small voltage. A one farad capacitor is extremely
large, and generally we deal with microfarads ( µf ), one millionth
of a farad, or picofarads (pf), one trillionth (10^{12}) of
a farad.
Consider the circuit of Fig. 9 again. Suppose
we cut the wires after all current has stopped flowing. The charge
on the plates is now trapped, so there is still a voltage between
the terminal wires. The charged capacitor looks somewhat like a
battery now.
If we connected a resistor across it, current would
flow as the positive and negative charges raced to neutralize each
other. Unlike a battery, there is no mechanism to replace the charge
on the plates removed by the current, so the voltage drops, the
current drops, and finally there is no net charge left and no
voltage differences anywhere in the circuit.
The behavior in time of
the current, the charge on the plates,
and the voltage looks just like the graph in Fig. 10. This
curve is an exponential function: exp(t/RC) . The voltage, current,
and charge fall to about 37% of their starting values in a time of R
×C seconds, which is called the characteristic time or the time
constant of the circuit.
The RC time constant is a measure of how
fast the circuit can respond to changes in conditions, such as
attaching the battery across the uncharged capacitor or attaching a
resistor across the charged capacitor. The voltage across a
capacitor cannot change immediately; it takes time for the charge to
flow, especially if a large resistor is opposing that flow. Thus,
capacitors are used in a circuit to damp out rapid changes of
voltage.
Combinations of
Capacitors
Like resistors, capacitors can be joined together in two basic ways:
parallel and series.
How to Calculate
Capacitance
of a Capacitor?
It should be obvious from the physical
construction of capacitors that connecting two together in parallel
results in a bigger capacitance value. A parallel connection results
in bigger capacitor plate area, which means they can hold more
charge for the same voltage. Thus, the formula for total capacitance
in a parallel circuit is: C_{T}=C_{1}+C_{2}...+C_{n}
,
the same
form of
equation for resistors in series, which can be confusing unless you
think about the physics of what is happening.
The capacitance of a series connection is lower than any capacitor
because for a given voltage across the entire group, there will be
less charge on each plate. The total capacitance in a series circuit
is : C_{T}={1{1C_{1}}+{1C_{2}}...+{1C_{n}}}.
Again, this is easy to confuse with the formula for parallel
resistors, but there is a nice symmetry here.
Learn More on Basics of Electronics:


















