Capacitors
2.0 Different types of capacitors and its capacitance.
2.0 Different types of capacitors and its capacitance.
A combination of two conductors placed close to each other in an insulator (or a vacuum), is called a capacitor.
One of the conductors is given a positive charge and the other one is given an equal negative charge.
The conductor with the positive charge is called positive plate and the other is called negative plate. The charge on the positive plate is called the charge on the capacitor.
Remember that the term charge on a capacitor does not mean that charge on it but it means a charge of the positive plate of the capacitor. The total charge on capacitor remains zero.
The potential difference between the plates is called the potential of the capacitor.
So the capacitor is an electrical device used to store electric potential energy in the form of charge. A capacitor is shown in the figure and the symbol used to represent capacitor is given in the figure.
Uses
The capacitor has a tremendous number of applications. In the flashlight used by the photographers energy and charge stored in a capacitor, is removed quickly. In other applications, energy is removed slowly.
Capacitance
It is the quantity of electric potential energy that a conductor can store in the form of charge at a given voltage.
When a charge $q$ is given to a conductor it spreads over the outer surface of the conductor due to repulsion between same nature of the charge. It wants to spare as far as possible to each other.
Then the whole conductor comes to the same potential (say $V$ ). This potential $V$ is directly proportional to the charge $q$ , i.e. , $$q \propto V$$
when the sign is removed a constant C is comes in picture. Hence , $$q = CV$$ or $$C = \frac{q}{V}$$
Here $C$ is called the capacitance of the capacitor. The SI unit of the capacitance is coulomb per volt which is written as farad (F). This is a large unit on normal scales and microfarad ($\mu F$) is used more frequently. Capacitance depends on the shape, size and geometrical placing and medium in which conductor is placed.
- One Farad Capacitance: When a capacitor (conductor ) having unit coulomb charge per unit voltage, a capacitance of conductor will be one farad.
- To put equal and opposite charge on two conductors, the may be connected to the terminals of a battery. We shall discuss in somewhat greater detail about the battery that why we state the following properties of an ideal battery.
- A battery has two terminals.
- The potential difference $V$ between the terminals is constant for a given battery. The terminal with a higher potential difference is called positive terminal and that with the negative potential is the negative terminal.
- The value of this fixed potential difference is equal to the electromotive force or emf of the battery. When two plates of a capacitor are connected to the terminals
- of a battery, the potential difference between the plates of the capacitor becomes equal to the emf of the battery.
- The total charge in a battery remains zero.
- When a charge $q$ passes through a battery of emf $\varepsilon $ from the negative terminal to the positive terminal, an amount $q\varepsilon $ is done by the battery.
An ideal battery is represented by the symbol shown in the figure. The potential difference between the facing parallel lines is equal to the emf $\varepsilon$ of the battery. The longer line is at the higher potential.
Calculation of Capacitance
The method for the calculation of capacitance involves integration of the electric field between two conductors or the plates which are just equipotential surfaces to obtain the potential difference ${V_{ab}}$. Thus,
$$\begin{equation} \begin{aligned} {V_{ab}} = - \int\limits_a^b {\overrightarrow E } .\overrightarrow {dr} \\ C = \frac{q}{{{V_{ab}}}} = \frac{q}{{ - \int\limits_a^b {\overrightarrow E } .\overrightarrow {dr} }} \\\end{aligned} \end{equation} $$
