mod 3 rg 3.9 capacitance and capacitors

Capacitors are components that store

charge in a circuit, usually for a short time

capacitors usually consist of two metal plates, or metal foils that are insulated from each other by a material called the

dielectric

The dielectric uses materials that

increase the strength of the electric field between the plates, which increases the amount of charge that can be stored at a given voltage.

The effectiveness of the dielectric material is measured by a quantity called the

“dielectric constant”.

Two alternative symbols can be seen in circuit diagrams depending on the country of origin, as illustrated below. The left diagram is by the International Electrotechnical Commission (IEC) standard (Europe) while the right one is by the American National Standards Institute (ANSI) standard (USA).

have a look to see the difference the American one is curvy

An electrolytic capacitor (polorised capacitor) has, in addition, a

‘+’ symbol next to the positive terminal.

When working with capacitors there are two, distinct hazards you must be aware of.

• Overheating due to excess voltage or reverse-polarity voltage

• Electric shock

Overheating is caused by an excessive or reverse voltage being applied to a capacitor. The capacitor can

expand quickly and explode. Such explosions have the potential to cause local damage, personal injury, and can even start a fire.

Capacitors are designed to work up to a particular voltage. This maximum value of voltage is marked or encoded on the body of the capacitor and must not

be exceeded

When choosing or replacing a capacitor, it is best to choose a capacitor with a voltage rating at least

twice that of the expected working value required in the circuit.

Electrolytic capacitors can only be used with

direct current and must be connected with the correct polarity.

Electrolytic capacitors have markings on their casings indicating

polarity

The positive terminal on a capacitor is marked with a ‘+’ symbol and

a longer positive lead

The negative terminal is marked with either

solid black line or a ‘–‘ symbol and a short lead.

Axial capacitors always have a positive terminal at the

crimped end of the cylinder.

Capacitors store electric charge and can store this charge for a long time. If an engineer begins work on a circuit that contains a capacitor that is not fully discharged, then they can

receive a dangerous electric shock. It is important to ensure that capacitors are fully discharged before commencing work, especially if the voltage exceeds 65 V.

When a voltage is applied across the two opposite plates of a capacitor, a current flows due to

the electric field generated between the plates as the charge accumulates. Eventually the current stops due to this accumulation of charge.

The amount of charge held by the plates depends on the following:

• Plate area

• The distance between the plates

  • The applied voltage

The amount of charge stored Q is proportional to

the applied voltage V

The constant of proportionality is given the symbol

C

The amount of charge stored Q =

C x V

The constant of proportionality C is referred to as

capacitance and its unit is the farad F

The farad can be expressed in terms of

ampere, seconds, and volts

(C) = AS/V = F

A capacitor has a capacitance of 1 farad if a current of 1 amp flowing for 1 second produces an increase in Potential Difference (PD) of

1 volt across the capacitor.

1 farad is a huge value of capacitance; therefore, values in electrical circuits tend to be in

microfarads, nanofarads, or picofarads.

The capacitance depends on three quantities:

• Area of overlap of the plates

• Distance between the plates

• Dielectric material used

it can be shown that C =

εA/d

Where C is the capacitance, in farads (F), A is the area of overlap of the plates in square metres (m²), d is the separation of the plates in metres (m) and ‘ε’ is the permittivity of the dielectric in farads per metre (F/m).

As two flat plates with large surfaces are not practical in most situations, capacitor plates are usually constructed from

several separate parallel layers, electrically connected. That way, the total area remains the same but the dimensions of the capacitor change.

The capacitor illustrated on the right-hand side of the graphic below is more compact than that on the left. Additionally, it makes use of

both sides of the plates; this gives it a greater overall area and, therefore, increased capacitance.

Another common method of capacitor construction is rolling the plates. This also allows

both sides to be utilised, thereby increasing capacitance.

Capacitors have a layer of dielectric material between the two plates. As well as increasing the capacitance that could be achieved using just air this also helps the capacitor withstand high voltages as the dielectric material can (normally) operate at

higher voltages than air without breaking down (sparking between plates).

vacuum has the lowest value of permittivity, which is a universal constant with the symbol ‘ε₀' and a value of 8.85 x 10^-12 F/m. This is also referred to as the

permittivity of free space.

other dielectrics have a permittivity greater than ε₀ and the multiplying factor is referred to as the

dielectric constant (or relative permittivity) of the material ε_r.

The dielectric constant for air is the same as that of a vacuum when measured to four significant figures.

‘ε₌ ε₀ε_r

For example, the dielectric constant of fuel is 2.7 so the permittivity of a dielectric consisting of fuel is

2.7 times greater than the permittivity of a dielectric consisting of air.

This principle is used for measuring fuel levels in the tanks of an aircraft. The process involves a tubular capacitor; fuel is used as the dielectric that fills the space between two concentric tubes. The fuel increases the dielectric constant and, therefore,

increases the capacitance of the sensor, which is measured electronically. The higher the fuel level, the greater the capacitance.

The water in the tank must be drained regularly to prevent it from falsifying

the tank measurement since water has a dielectric constant of 80.

capacitors that have two conducting layers between the paper foil or the plastic film (dielectric). These can consist of metal foil or an evaporated metal layer. This type of capacitor is

non-polar (either plate can be made positive with respect to the other plate) and can be used with direct or AC voltage. There are paper or film capacitors for all capacitance values.

the electrolytic capacitor has layers of

aluminium foil, forming the positive plate. The second conducting layer is a thickened or solid electrolyte, forming the negative plate. The dielectric forms as a thin aluminium-oxide layer between the two, but only if the polarity is maintained (that is, the aluminium must be positive with respect to the electrolyte).

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Operating an electrolytic capacitor with Alternating Current (AC) or connecting it to Direct Current (DC) voltage with the wrong polarity will

destroy the dielectric and permanently damage the capacitor.

Electrolytic capacitors with DC voltage are used to provide

high capacitance in a small space (flashguns, capacity filtering of DC voltage, etc.)

Capacitors can be used in various circuits to

accept or reject certain frequencies of AC input If the capacitance can be varied, the circuit can be tuned to select a certain frequency or band of frequencies

In the capacitor, shown in the left image below, the capacitance can be varied by turning the shaft and varying the area of plate overlap; this setup was used in

old-fashioned radio sets.

The variable capacitor, shown below on the right side of the picture would be used as a trimmer for setting or calibrating a component or system. Trimmer capacitors are small-size variable capacitors comprising of

two metal plates normally divided by a slim piece of mica.

The capacitance is altered by changing the space between the plates by a tiny screw that pushes the plates together. Trimmer capacitors are widely employed in

radio receivers to allow fine modification of the capacitance of the tuned circuit.

The capacitance value and tolerance are marked on the capacitor’s body using a

colour code

The colours painted on the capacitor’s body are called

colour bands Each colour band represents a different number.

The colour codes used to represent the capacitance values and tolerance are similar to those used for resistance values and tolerance. Generally, capacitors are marked with

four or more colour bands.

In a four-colour band capacitor, the first and second colour bands coated on the capacitor represent the

first and second digits of its capacitance.

The third colour band represents the

decimal multiplier,

the fourth colour band represents

tolerance

The value is given in

picofarads (10^-12 F)

Where a fifth colour band is present in a capacitor, (Type K) this denotes

the voltage rating of a capacitor. The voltage rating indicates the maximum voltage for the capacitor.

A capacitor should not be subjected to a voltage any greater than its voltage rating - doing so may

permanently damage the capacitor.

It is good practice when selecting capacitors for a circuit, to choose capacitors with a voltage rating of approximately

twice the expected working voltage

Rule of thumb: voltage rating = 2 x working voltage.

The working voltage is the maximum voltage that the capacitor will be subjected to

under normal operation of the circuit.

When capacitors are connected in series, capacitance is

reduced.

opposite to a resistor in series sum of the capacitances is smaller than that of the

smallest individual capacitor

the formula for capacitance in series is

1/CT= 1/C1 + 1/C2 + 1/C3

(you must flip at the end to get CT on its own)

The sum of the voltages across series capacitors is equal to the

total voltage across the equivalent capacitor C_T

The voltages are distributed in inverse proportions to the capacitances, so the

largest capacitors will have the smallest voltage across them and vice versa.

f n capacitors are connected in parallel, their capacitances must be

added together to find the total capacitance C_T

( opposite to resistors)

The individual voltages across parallel capacitors are equal to the total voltage across the equivalent capacitor C_T. The voltages are

all the same when capacitors are connected in parallel.

Many applications involve a capacitor being charged and discharged in part of a circuit. Both the charging and discharging of a capacitor, through the resistance of the connected circuit, do not happen instantly but

over a period of time

The time taken for a capacitor to either charge or discharge is governed by the

mathematical law of exponential decay, and by the values of capacitance, resistance and Potential Difference (PD).

When connecting a completely discharged capacitor to a battery, the initial current will be extremely high, as the capacitor initially

has no PD across it.

To limit this initial high current current form a discharged capacitor, we always

use capacitors with a resistor in series. This means the initial current depends only on the resistor.

n a series connection, the voltage of the battery is divided between the loads. When first switched on, the capacitor has no charge and, therefore,

it has no voltage across it. The whole battery voltage must be across the resistor. In line with Ohm’s Law, "the resistor limits the current". The initial current is given by

I = V/R

As the capacitor becomes charged, the voltage across it rises. Applying Kirchhoff's second law, the sum of the voltages across the resistor and capacitor must

equal the supply voltage.

Consequently, the higher the capacitor voltage the lower the resistor voltage and the lower the current. This is because

the current is still limited by the resistor, but the voltage across the resistor is now lower so the current will also be lower. As a result, the current steadily falls with time.

The higher the capacitance, and the resistance, the

longer the charging time will be.

The product of resistance and capacitance is known as the

time constant.

The time constant is a useful estimate of

the time taken to charge or discharge a capacitor which is in series with a resistor.

Time constant =

RC

Where ‘R’ is the resistance in ohms (Ω) and ‘C’ is the capacitance in farads (F)

time constant also describes how capacitor voltage varies during charging and discharging. During charging

the current decreases as the capacitor’s voltage increases.

If one plots this current and voltage against time, the graph describes

an exponential decay. Similarly, the voltage of the capacitor shows exponential growth.

After one time constant has passed, the current will fall to ad the voltage will rise

37% of its initial value, and the voltage will rise to 63% of its final value (the supply voltage).

After two time constants the current will fall to

37% of 37% of its initial value, i.e. 37% x 37% = 14% of its initial value. This is true for any initial value of the current.

If we continue with this logic, after five time constants have passed the current will have fallen to

(37%)⁵ which is equal to 0.7% of its initial value

After five time constants have passed, the capacitor is considered to be

fully charged

1 time constant

Capacitor Voltage (% Charged)	Circuit Current (% Remaining)

63.2%

36.8%

2 time constant

Capacitor Voltage (% Charged)	Circuit Current (% Remaining)

86.5%

13.5%

3 time constant

Capacitor Voltage (% Charged)	Circuit Current (% Remaining)

95.0%

5.0%

4 time constant

Capacitor Voltage (% Charged)	Circuit Current (% Remaining)

98.2%

1.8%

5 time constant

Capacitor Voltage (% Charged)	Circuit Current (% Remaining)

99.3% (Considered full).

0.7% (Considered stopped)

f the capacitor is discharged through the same resistor (having removed the battery from the circuit) then

the discharge current follows exactly the same graph as shown above; however, the voltage will not rise but falls in the same way the current does.

At t=RC, the capacitor holds 37% of its initial charge; after t=5RC it is discharged completely.

Visual inspection of capacitors can only reveal bulging of the casing and electrolyte leakage.

An ohmmeter can be used to

test a capacitor. The capacitor charges from the internal battery of the ohmmeter. Select [Rx1] or [Rx10] for small values (<1uF), and [Rx100] or above for a large value capacitor (>1uF).

First, discharge the capacitor by touching the capacitor’s leads together.

Connect the positive probe of the ohmmeter to the positive lead of the capacitor, and the negative probe to the negative lead. The meter pointer should move to zero resistance and then swing to infinity as the capacitor charges. Discharge the capacitor again and repeat the test, this time touching the negative probe with the positive lead. The meter’s pointer should move to zero and then swing close to infinity.

These results indicate that the capacitor is probably working.

A capacitor with an open circuit (fault) will give

an infinite resistance on both readings.

A shorted capacitor (fault) will show

a zero or near-zero reading and will never swing to infinity.

A good capacitor that can store a charge with less leakage will show

an infinite resistance reading. This means there will be no current flow after it is fully charged.

Small capacitors charge extremely quickly and require

a dedicated LCR tester

an LCR tester is a meter that can measure the inductance (L), capacitance (C) and resistance (R) of a circuit..

Capacitor failures can be categorised into two main areas:

• Catastrophic Failures: Generally caused by a short circuit through dielectric breakdown or open circuits caused by connection failures.

• Degradation Failures: Usually caused by a gradual decrease in leakage resistance, resulting in an increase in leakage current, equivalent series resistance, or dielectric absorption.

Another possible failure is excessive equivalent series resistance. This can be caused by

a defective lead to plate contact, resistive leads, or resistive plates; it only occurs in AC circuits.

More than 40% of all defective capacitors have

excessive leakage current; electrolytic capacitors are particularly susceptible.

Dielectric absorption, which makes up 25% of defects, occurs mainly in

electrolytic capacitors when they do not completely discharge during use and retain a residual charge. This can be dangerous, in that a capacitor that appears to have been discharged can still hold a large charge when the leads are disconnected from each other after shorting.