Capacitors

Monday, 20 August 2018

1:33 PM

A capacitor is a circuit element that stores energy in its electric field

It consists of two conducting plates separated by an insulator (or a dielectric)

Usually, these plates are aluminium foil
Dielectrics are often air, ceramic, paper, plastic or mica

 

When a voltage source  is connected to the capacitor, the source deposits a positive charge  on one plate, and a negative charge  on the other plate

The charges will be equal in magnitude on both plates

The amount of charge is proportional to the voltage

 

 

Capacitance is the ratio of voltage to charge across a capacitor, and is given the symbol

Capacitance is measured in farads , which is coulombs per volt.

 

 

Capacitance depends on the physical dimensions and geometry of the capacitor.

For parallel-plate capacitors, the capacitance is given as

 

Where

 - Permittivity of the dielectric

 - Surface area of each plate

 - distance between the plates

 

 

 

 

Capacitors are available in different values and types.

They are described by their dielectric material

They are usually rated in picofarads (), to microfarads ().

They are used to block DC and pass AC signals, shift phase, store energy, suppress and filter noise, etc

 

Convention - Passive sign convention applies to capacitors as well

If , the capacitor is being charged (absorbing energy)

If , the capacitor is being discharged (supplying energy)

 

For capacitors in the range of  particularly electrolytic ones, the polarity is already assigned (on an electrolytic capacitor, the negative terminal is physically marked)

 

 

Equations

Charge = Capacitance x Voltage

Differentiation wrt time gives

Current is the rate of change of charge, so

Voltage is then

Where  is called the intial voltage, or initial conditions at time

Instantaneous power delivered to the capacitor

The energy stored in the electric field that exists between the plates of the capacitor can be then calculated as

 

If , then

 

Properties

A capacitor is an open circuit to DC voltage.

This is because of the equation,

At a constant voltage, there is no change in voltage, and

Therefore,

 

 

An ideal capacitor does not dissipate energy, energy is absorbed from a circuit, stored in an electric field, and then released back into the circuit

 

However, a real capacitor has a parallel-model leakage resistance, leading to a slow loss of the stored internal energy

 

 

Capacitors in Parallel

Capacitors can be added in series or parallel

For capacitors in parallel, the voltage is the same across each capacitor

Applying KCL and current-voltage relation  for capacitors

 

 

Capacitors in Series

Current is the same through each capacitor