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                           Fig - 1 : A simple capacitor connected to a battery through a resistor

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 like-sign charges on each terminal want to get away from each other. In addition to that repulsion, there is an attraction to the opposite-sign 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. 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=C₁+C₂...+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{1C₁}+{1C₂}...+{1C_n}}.

Again, this is easy to confuse with the formula for parallel resistors, but there is a nice symmetry here.