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Uses of Capacitorswww.curriculum-press.co.uk Number 84

FactsheetPhysics

Factsheet 29 provided a thorough discussion of capacitor theory. It maywell be worth looking through this again.

In this Factsheet we will be looking at the ways that capacitors can be usedin electronic circuitry, and the types of capacitors that are in common use.

A brief summary of relevant theory1. Charge and discharge rates:

V C

R

+

-

Charging

C R+-

Discharging

A capacitor charges or discharges through a resistor following an exponentialcurve. The time constant, T, is defined as: T = RC (s)

The discharge graphs resemble:

V, I, Q

t

Things are slightly more complex for the charging graphs. The p.d. andcharge stored increase as the charging current falls:

I

t

t

V,Q

In each case the current drops to 0.37 of its initial value after one timeconstant: e-t/RC = e-1 = 0.37

Most uses of capacitors involve this time constant. It can be seen thatincreasing R or increasing C results in a larger time constant. The charge anddischarge rates change more slowly.

2. Capacitance and Energy:

When a capacitor C is charged to a potential difference V, a charge Q isstored in it. Q = CV, or C = Q/V (farads)

The energy stored on this capacitor can be written:

E = ½CV2 = ½QV = ½Q2/C (joules)

3. Reactance:In an a.c. circuit, a capacitor C has a reactance.

XC =

1 (ωC)

(ohms)

Where ω is the angular frequency (ω = 2πf).

Reactance for a capacitor is equivalent to resistance for a resistor.

Example:(a) To what fraction of its original voltage does a discharging

capacitor drop after 3 time constants (T=3RC)?(b) How many time constants does it take for the voltage to drop to

25% of its initial value?

Solution:(a) e-3T/RC = e-3 = 0.050

(b) e-t/RC = 0.25, -t

RC =

ln 0.25 = -1.39, t = 1.39RC = 1.39T

.

At very high frequencies the capacitor acts as a short circuit; atvery low frequencies the capacitor blocks most of the current.

Example:(a) A 1.5µµµµµF capacitor is placed in a mains circuit (f=50Hz).

Find its reactance.(b) It is then placed in a d.c. circuit (batteries). What is its

reactance now?

Solution:(a) X

C = 1/(ωC) = 1/(2π × 50 × 1.5×10-6) = 2.1kΩ

(b) XC = 1/(ωC) = Infinity, as the frequency is zero.

In a d.c. circuit, the capacitor does not let any current through.

84. Uses of Capacitors Physics Factsheet

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Uses of Capacitors

1. CouplingBecause a capacitor blocks d.c. signals, it can be used between stages of anamplifier, or to connect the amplifier to a loudspeaker. Only the a.c. signalcan get through.

R

C

Stage 2Stage 1

If the input signal is a square wave:

0V

Input Current

Output Current 0V

It is important that the time constant of the coupling circuit (RC) is muchgreater than the period of the input signal. If the capacitor were to becomesignificantly charged (or discharged) during each half cycle, then the currentflow would fall. This would cause distortion in the output.

0V

Input Current

Output Current(RC too small)

0V

Obviously this would not be acceptable.

Only the varying component of a signal can travel through acapacitor.

2. SmoothingA diode bridge rectifier changes a.c. voltage (e.g. mains) into d.c. voltage.This is often required in electronic circuitry. However the d.c. output ofthe rectifier is not steady:

A large capacitance across the output stores charge, which can then bedischarged through the load as the output voltage from the rectifier falls.

d.c. supplyOutput Load R

The voltage across the load is smoothed by this extra flow of charge.

V

t

C charging C discharging

There is still a slight ripple in the voltage. The larger the capacitance, thesmaller the ripple will be. If the load only requires a small current flow (e.g.electronics), then the smoothing can be almost perfect.

A high value capacitor can be used to smooth d.c. voltagefor many applications.

3. Energy dischargeIn certain devices, it is important that all of the energy is supplied in asudden pulse. Examples are flashguns and some types of lasers. Thisrequires a very high current flow for a very short period of time.Power supplies cannot do this.

The internal resistance, r, limits the flow of current,

I = V

(R+r) , restricting the rate of energy transfer.

However, if energy is stored on a capacitor, then the discharge current canbe very large, as long as the resistance of the load, R, is very small. Theinitial current flow is given by I=V/R. If the load is tiny, then the rate ofenergy transfer P=V2/R can be very large.

The lack of significant internal resistance means that acharged capacitor can deliver energy very quickly (for a short periodof time).

4. OscillationThe charge and discharge rates for a capacitor circuit can be used to producean alternating signal. The frequency depends on the components chosen.

rV

Load R

-+

V1

V2 R

1

R2

V0

0V

C

R

C

Physics Factsheet

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84. Uses of Capacitors

This is an astable multivibrator. When V1 becomes larger than V

2 , the

output Vo instantly becomes negative. Capacitor, C, discharges through

resistor, R, until V1 becomes less than V

2 . The output V

o jumps to a

positive value. The capacitor charges up (through R) until V1 becomes

greater than V2 , forcing V

o to go negative again.

The output voltage is a square wave.

V0

t

The frequency is controlled by the values of R and C, as time constant RCdetermines the rate of charging and discharging (and thus the rate at whichV

1 changes). Often R is a variable resistor, allowing the operating frequency

to be adjusted.

An RC circuit can be used to determine the rate of switchingin many types of oscillating circuits.

5. TunersA traditional and simple tuning circuit for radios, televisions, etc, relies ona capacitor and inductor in parallel.

All the carrier frequencies are picked up by the aerial. By choosing thecorrect values for C and L, the device can be tuned to a selected frequency.

Output

fR

f

The reactance of the inductor increases with frequency; the reactance ofthe capacitor decreases with frequency. The maximum voltage across thetuner occurs when: 1

fR =

(2π√LC)

fR is the resonant frequency.

Output

Aerial

L

An L-C parallel circuit allows us to tune to a selected frequency.A variable capacitor makes tuning through a range of frequenciespossible.

Some useful capacitorsThe basic capacitor has two conducting plates separated by a dielectricmaterial. The capacitance is given by:

C = Aεoε

r

d A is the area of each plate ε ε ε ε ε

o is the permittivity of free space

ε ε ε ε εr is the relative permittivity of the dielectric

d is the separation of the plates.

There are different ways that practical capacitors can be constructed.

1. Film capacitors

paper

metal foil

paper

metal foil

The paper and metal strips are rolled into a cylinder, forming large areas ofmetal separated by waxed paper as the dielectric. These capacitors arevery cheap. They make good general-purpose capacitors.Often plastic films such as polycarbonate and polystyrene are used insteadof paper, as they improve the frequency response.

2. Electrolytic capacitorsOnce again thin strips of material are rolled into a cylinder to form a largearea in order to maximise capacitance. But this time the dielectric is just athin film of aluminium oxide formed on the positive strip of aluminium foil(the anode).

paper soaked in electrolyte

aluminium foil

paper soakedin electrolyte

aluminium foil

A chemical reaction forms the oxide layer. It may be less than 10-6m thick,greatly increasing the capacitance. Electrolytic capacitors routinely havecapacitances of hundreds of microfarads, or even more.

Their high capacitance makes them very useful in smoothing and couplingcircuits. However they have a constant leakage current (limiting their use inlow power electronic circuits), and must be put in the circuit the correctway round to avoid damage (they are polarised).

3. Variable air capacitorsTuning circuits require a capacitor whose value can be changed. The variableair capacitor accomplishes this by changing the effective area of the platesfacing each other.

Turning the knob rotates one set of plates, changing the effective area. Theactual capacitance is small. The important point is that it can be varied.

C

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84. Uses of Capacitors Physics Factsheet

Questions1. In a coupling circuit, sketch the output current (from a square wave

input) if the time constant is much smaller than the period of the inputsignal.

2. In a smoothing circuit, the load requires a steady current of 0.5 amps.The smoothing capacitor holds a maximum charge of 2.4×10-4 coulombs.Is the smoothing likely to be very effective at mains frequency?

3. Two strips of paper and two strips of metal foil are rolled up to makea paper capacitor. Each strip is 50cm long, 2cm wide, and has a thicknessof 0.1mm. Find the diameter of the cylinder formed.

4. Give one advantage and one disadvantage of electrolytic capacitors.Where are they used?

5. Two ways that capacitance can be maximised are by increasing the areaof the plates or by decreasing the separation of the plates. What methodsare used in film, electrolytic, and air capacitors to maximise capacitance?

Answers1.

The capacitor becomes completely charged or discharged, and the currentdrops to zero.

2. For mains electricity, one-half of a cycle lasts 0.01s.The charge required to provide the current in this time:Q = It = 0.5 × 0.01 = 5 × 10-3 coulombs.Although the capacitor only has to supply the charge for part of thecycle, there is far too much charge required. The capacitor is much toosmall.

3. Volume cylinder = Volume rectangle(choose cm as unit)πr2l = lwt, πr2 = wt, r2 = 4 × 50 × 0.01 / πr2 = 0.64cm2, r = 0.80cm d = 1.6cm.

4. Advantage – large capacitance.Disadvantage – leakage current, polarised.Used in smoothing and coupling circuits.

5. Film capacitor – large area.Electrolytic capacitor – large area, small separation.Air capacitor – neither.

Acknowledgements:This Physics Factsheet was researched and written by Paul FreemanThe Curriculum Press,Bank House, 105 King Street,Wellington, Shropshire, TF1 1NUPhysics Factsheets may be copied free of charge by teaching staff or students, provided that their school is a registered subscriber.No part of these Factsheets may be reproduced, stored in a retrieval system, or transmitted, in any other form or by any other means, without the prior permission of the publisher.ISSN 1351-5136