# Capacitor

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A capacitor is an arrangement of two conductors carrying charges of equal magnitudes and opposite sign and separated by an insulating medium. The net charge on the capacitor as a whole is zero. When we say that a capacitor has a charge Q, we mean that the positively charged conductor has charge +Q and negatively charged conductor has charge -Q. The positively charged conductor is at higher potential than the negatively charged conductor. The potential difference V between the conductors is proportional to the charge magnitude Q and the ratio Q/V is known as capacitance of the capacitor denoted by C.

$C = \frac{Q}{V}$

Unit of capacitance is farad(F). The capacitance is usually measured in microfarads(μF). In a circuit, a capacitor is represented by the symbol:. Capacitors work as a charge storing or energy-storing devices. A capacitor can be thought of as a device which stores energy in the form of electric field. Energy stored in a capacitor is denoted by U. If V is the potential difference(voltage) across the capacitor and Q is the charge on the capacitor and C is the capacitance of capacitor, then:

$U = \frac{1}{2}CV^2$, or
$U = \frac{1}{2} \frac{Q^2}{C}$, or
$U = \frac{1}{2}QV$.

## Parallel plate capacitor

The parallel plate capacitor consists of two metal plates placed parallel to each other and separated by a distance that is very small as compared to the dimension of the plates. The electric field between the plates is given by:

$E = \frac{\rho}{k \epsilon_{o} }$

where ρ: surface charge density on either plate

k: dielectric constant of the medium between plates

If d is the separation between the plates and A is the area of each plate, the potential difference (V) between plates is given by:

V = Ed
$V = \frac{\rho}{k \epsilon_{o} } d = \frac{Q}{k\epsilon_{o} A} d$
$C = \frac{k \epsilon_{o} A }{d}$ for parallel plate capacitor.