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A capacitor has a capacitance of one farad when one coulomb of charge causes a potential difference of one volt across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (μF), nanofarads (nF) or picofarads (pF).
When the voltage across a capacitor changes, the capacitor will be charged or discharged. The associated current is given by
where i is the current flowing in the conventional direction, and dV/dt is the time derivative of voltage.
Moving a charge Q across a potential difference of V requires an energy QV; here the charge is CV but the energy is not CV², but less (in fact half of that) because while charging the potential difference is not yet equal to the final value; therefore (simple) integration is required to find the formula above.
The capacitance of a parallel-plate capacitor is approximately equal to the following:
where C is the capacitance in farads, ε0 is the electrostatic permittivity of vacuum or free space, εr is the dielectric constant or relative permittivity of the insulator used, A is the area of the each of the two plates, and D is the distance between the plates.
Electrons cannot pass from one plate of the capacitor to the other. When a voltage is applied to a capacitor, current flows to one plate, charging it, while flowing away from the other plate, charging it oppositely. In the case of a constant voltage (DC) soon an equilibrium is reached, where the charge of the plates corresponds with the applied voltage, and no further current will flow in the circuit. Therefore direct current cannot pass. However, effectively alternating current (AC) can: every change of the voltage gives rise to a further charging or a discharging of the plates and therefore a current. The amount of "resistance" of a capacitor to AC is known as capacitive reactance, and varies depending on the AC frequency. Capacitive reactance is given by this formula:
It is called reactance because the capacitor reacts to changes in the voltage.
Thus the reactance is inversely proportional to the frequency. Since DC has a frequency of zero, the formula confirms that capacitors completely block direct current. For high-frequency alternating currents the reactance is small enough to be considered as zero in approximate analyses.
The impedance of a capacitor is given by:
Hence, capacitive reactance is the negative imaginary component of impedance.
Important properties of capacitors, apart from the capacitance, are the maximum working voltage and the amount of energy lost in the dielectric. For high-power capacitors the maximum ripple current and equivalent series resistance (ESR) are further considerations.
Capacitors can be fabricated in semiconductor integrated circuit devices using metal lines and insulators on a substrate. Such capacitors are used to store analogue signals in switched-capacitor filters, and to store digital data in dynamic random-access memory (DRAM).
Leyden jar, the first form of capacitor, was invented at Leiden University in the Netherlands. It was a glass jar coated inside and out with metal. The inner coating was connected to a rod that passed through the lid and ended in a metal ball.