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Introduction to the Capacitor in Electrical Engineering

​We can think of capacitors are short term ‘charge-stores’. In other words, capacitors just store charge inside them. A capacitor consists of two metal plates separated by a layer of insulating material called a dielectric.

There are 2 types of capacitor:

  1. Electrolytic capacitors. These hold much more charge and must be connected with the correct polarity, otherwise they can explode.
  2. Non-electrolytic. These hold less charge and can be connected either way round in a circuit.
, Capacitors Explained for Engineers

How Does a Capacitor Work?

When two conducting plates are connected to a battery, electrons move towards one plate. The positive plate loses electrons , eventually leaving both plates with equal and opposite charge, +Q and -Q. When a capacitor is charged, we say that the capacitor has charge Q.

, Capacitors Explained for Engineers

Define Capacitance

Capacitance, C = “the charge, Q, required to cause potential difference, V, in a conductor. It is measured in Farads”.

“1 Farad is the capacitance of a conductor, which has potential difference of 1 volt when it carries a charge of 1 coulomb”.

, Capacitors Explained for Engineers

Charging a Capacitor Using D.C.

At any time, t, after the switch is closed, the charge, Q, on the capacitor can be calculated using Q=It where I = the current (Amps).

The variable resistor can be altered to keep the current constant.

, Capacitors Explained for Engineers

Plot a graph of capacitance against voltage and since:

, Capacitors Explained for Engineers

The gradient of the graph will equal the capacitance of that capacitor.

Charge Stored in a Capacitor

Electrical potential energy is stored when a capacitor is charged.

, Capacitors Explained for Engineers

The area under this graph is equal to the energy stored = (½bh)

We can combine previous equations to give the following:

, Capacitors Explained for Engineers
, Capacitors Explained for Engineers

Charging and Discharging a Capacitor

When discharging, the current decreases with the potential difference, p.d. This decrease is exponential as can be seen below. Q0, V0 and I0 are all the initial charge, voltage and current through the capacitor at the initial discharge.

, Capacitors Explained for Engineers

Decay Curve

Let us now examine the process of discharging the capacitor. Charge, Q, falls to 1/e of its initial value in a time equal to the time constant, RC.

, Capacitors Explained for Engineers

When the initial charge is Q0,

  • After RC seconds = 0.37 x Q0
  • After 2RC seconds = 0.37 x 2 x Q0
  • After nRC seconds = 0.37n x Q0.

The time taken to halve, T½, is always the same:

, Capacitors Explained for Engineers
, Capacitors Explained for Engineers

Example of Capacitors in Series and Parallel

, Capacitors Explained for Engineers
, Capacitors Explained for Engineers

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