CAPACITANCEPrepared and presented by Doren Nedrick

What is a Capacitor?An electronic device designed to store electric charge. Basically it consists of two metal plates separated by an insulator material called the dielectric.

metal plate Y

metal plate X

Types of CapacitorsCan be of fixed or variable value (Fixed and variable capacitor ). Fixed capacitors have a specific single value of capacitance. Fixed capacitors can be polarized - electrolytic ( ) or non polarized ( ) non polarized types can be connected either way round (nonelectrolytic). Polarized types have a positive and a negative terminal and must be connected so that there is DC through them in the correct direction.

Practical Capacitors

Variable Capacitors

Nonelectrolytic or electrolytic refers to the structure of the dielectric.Electrolytic capacitors use only polarized direct current and can, and often do, explode when an alternating or opposite voltage is applied to themExamples of electrolytic (polarized) capacitors are: Aluminium and tantalum and examples of nonelectric capacitors are polyester, Mica and Ceramic.

Types of Capacitors Continued

CapacitanceThe capacitance (C) of a capacitor measures its charge storing ability and is measured in farads (F).The charge stored by a capacitor can be found by using the formula Q = C x V Where Q = charge (measured in coulomb C), C = capacitance (in Farads and V = voltage (in volts).

The FaradIt is 1 farad (F) if it stores a charge of 1 Coulomb when the p.d. across it is 1Volt. If the charge is 6C when the p.d. is 2V, then C = 6C/2V = 3F. 1 Farad is a large value of capacitance hence smaller units are:1 microfarad (F) = 10-6 F1 nanofarad (nF) = 10-9 F1 Picofarad (pF) = 10-12 F

ExampleHow much charge is stored in a 10uF capacitor with 50V across it?C = 10 x 10-6 FV = 50VQ = ?Q = C x VQ = 10 x 10-6 F x 50V = 500 uC

Activity1. How much charge is stored in a 6800uF capacitor with 50V across it?2. A capacitor stores 10, 000uC of charge with 20V across its plates. Calculate C.3. What voltage will be across the plates of a 2uF capacitor if it stores 100uC of charge?

Construction and OperationBasically it consists of two metal plates separated by an insulator called the dielectric. When connected to a battery, the positive of the battery attracts electrons from plate X and the negative repels electrons to plate Y. Positive charge (deficit of electrons) builds up on X and an equal negative (excess of electrons) builds up on Y.

metal plate X

metal plate Y

Construction and OperationDuring the charging there is a brief flow of electrons round the circuit from X to Y. Charging stops when the p.d. between X and Y equals (and opposes) the e.m.f. of the battery.

metal plate X

metal plate Y

Effect of a capacitorDuring the charging there is a brief flow of electrons round the circuit from X to Y. Charging stops when the p.d. between X and Y equals (and opposes) the e.m.f. of the battery.

Effect of capacitor (contd)The process takes time, i.e. the response of a capacitor to a change of p.d. is not immediate. If the connections to the battery are removed, the charge may take a long time to leak away from the capacitor unless a conductor is connected across it.A capacitor blocks the flow of direct current A capacitor allows alternating current to pass through

Factors affecting the capacitance of a capacitor Increasing the Cross Sectional Area (CSA) of the platesDistance between the plates Type of dielectric material used

Cross Sectional AreaAll other factors being equal, greater plate area gives greater capacitance; less plate area gives less capacitance. Explanation: Larger plate area results in more field flux (charge collected on the plates) for a given field force (voltage across the plates)

Distance Between the PlatesAll other factors being equal, further plate spacing gives less capacitance; closer plate spacing gives greater capacitance. Explanation: Closer spacing results in a greater field force (voltage across the capacitor divided by the distance between the plates), which results in a greater field flux (charge collected on the plates) for any given voltage applied across the plates.

Type of Dielectric Material Used All other factors being equal, greater permittivity of the dielectric gives greater capacitance; less permittivity of the dielectric gives less capacitance. Explanation: Some materials offer less opposition to field flux for a given amount of field force. Materials with a greater permittivity allow for more field flux (offer less opposition), and thus a greater collected charge, for any given amount of field force (applied voltage).

Permittivity of dielectric materials"Relative" permittivity means the permittivity of a material, relative to that of a pure vacuum. The greater the number, the greater the permittivity of the material. Glass, for instance, with a relative permittivity of 7, has seven times the permittivity of a pure vacuum, and consequently will allow for the establishment of an electric field flux seven times stronger than that of a vacuum, all other factors being equal.

PermittivityMaterial Relative permittivity (dielectric constant) Vacuum ------------------------- 1.0000 Air ---------------------------- 1.0006 Waxed paper -------------------- 2.5 Hard Rubber -------------------- 2.5 to 4.80 Wood (Oak) --------------------- 3.3 Wood (Maple) ------------------- 4.4 Glass -------------------------- 4.9 to 7.5 Wood (Birch) ------------------- 5.2 Mica, ---------------- 5.0 to 8.7 Porcelain, ------------ 6.5 Alumina ------------------------ 8.0 to 10.0

Energy StoredA charged capacitor stores electrical energy (energy of moving electrons) and can be found by using the formula below:W = x C x V2 or x Q x V (Since Q = C x V) Where W = E = work done or energy, C = Capacitance and V = Voltage

ExampleCalculate the energy stored by a capacitor if it stores 1000uC of charge when the voltage across it is 50V.Q = 1000uCV = 50VW = ?W = x Q x VW = x 1000 x10-6 x 50VW = 25 000uJ

ExampleCalculate the capacitance of the capacitor?Since Q = C x VThen C = Q/V C = 1000uC/ 50V C = 20uF

ActivityA capacitor stores 10,000C of charge with 20V across its plates. Calculate the capacitance C and the energy stored by this capacitor.How much charge is stored in a 6800F capacitor with 50V across it? How much charge is stored by the capacitor?What voltage will be across the plates of a 2F capacitor if it stores 100C of charge? Calculate the energy stored by this capacitor?

Controlling the time taken to charge a capacitorThe time taken to charge to its maximum can be varied by placing a resistor in series.

Time Constant ContdIn this circuit, when S is in position 1, C charges through R from the supply. The microammeter measures the charging current I and the voltmeters record the p.d.s VC and VR across C and R respectively at different times (t).

Graph of charging CharacteristicsGraphs like those in Fig. a and b can be plotted from the results and show that:I has its maximum value at the start and decreases more and more slowly to zero as C charges up; Vc rises rapidly from zero and slowly approaches the supply voltage V which it equals when C is fully charged; and VR behaves like I.

Capacitor Discharging In A CR Circuit Fig. 12.1, when S is moved from position 1 to position 2 The capacitor discharges through R. If graphs of I, Vc, and VR are plotted as before, they are again exponential curves, like those in Figs. 4a and b.

Capacitor Discharging In A CR Circuit They show that:(i) I, the discharge current, has its maximum value at the start but is in the opposite direction to the charging current (as is VR); and(ii) VC and VR fall as C discharges and are equal and opposite at all times.

Time Constant of a CR CircuitThe charging and discharging of a capacitor through a resistor do not occur instantaneously. The time constant is a useful measure of how long these processes take in a particular CR circuit.Charging If a capacitor of capacitance C is charged at a constant rate through a resistor of resistance R by a steady current I, it would be fully charged with charge Q and p.d. V after a time t where t = CR seconds if C is in farads and R in ohms.

Examplet = C x Rt = 1uF x 1000T = 1000uS or 1mS or 0.001S

Example contdThis time constant of 1mS is a measure of how long it takes for a 63.2% change to occur. After 5 RC time constants have elapsed, the voltage across C is practically equal to its steady state value of 12V.Vmax = 5 x 1msVmax = 5mS

ActivityWhat is the time constant for a circuit in which C = 1F and R = 1M(b) How long will it take to reach its maximum current?

Why should a capacitor with a working voltage of 250V not be used on a 230V ac supply?

Capacitors in parallelVoltage in parallel equalQ1 = C1 x VTQ2 = C2 x VTQ3 = C3 x VTQT = CT x VTQT = Q1 + Q2 + Q3

CT x VT = (C1 x VT) + (C2 x VT) + (C3 x VT)Divide both sides by VT well achieveCT = C1 + C2 + C3Connecting capacitors in parallel is equivalent to increasing its plate area. Therefore, the total capacitance for parallel connected capacitors is the sum of the individual capacitances.

Example Find: CT, QT, Q1, Q2, Q3, E1, E2, E3, ETCT = C1 + C2 + C3CT = 10F + 20F + 50FCT = 80FQT = CT x VT = 80F x 12V = 960C

Q1 = C1 x VT = 10F x 12V = 120C

E1 = Q x VT = x 120C x 12V = 720J

ActivityThree capacitors: C1 = 0.5uF, C2 = 1.5uF and C3 = 2uF are connected in parallel to a battery of 12V. Calculate the total capacitance The total charge stored by the networkThe charge stored by each capacitor The energy stored by the entire circuitThe energy stored by each capacitor

Capacitors in seriesQT = Q1 = Q2 = Q3VT = V1 + V2 + V3QT = QT + QT + QTCT C1 C2 C3Divide both sides by QT well achieve1 = 1 + 1 + 1CT C1 C2 C3Connecting capacitors in series is equivalent to increasing the distance between the capacitor plates

ExampleFind: CT, QT, V1, V2, V3, E1, E2, E3, ET

ActivitySolve: Q, VC1, VC3, CT, VT and the energy stored by C3

Capacitance in a.c. and d.c. circuit

Capacitive ReactanceWhen an alternating voltage is applied across the plates of a capacitor, the capacitor will alternatively charge and discharge.This means there will be charge and discharge current flowing to and from the plates of the capacitor. How much current flows for a given amount of applied voltage is determined by the capacitive reactance (XC)

Capacitive ReactanceXC = 1/(2 f C)

Example:A capacitor of 100F is placed across a 250V, 50Hz supply. Calculate the current flowing in the circuit.

Practical CapacitorsWhen choosing a capacitor two factors need to be considered, apart from its value and tolerance.1. The voltage rating: this is the maximum voltage (d.c. or peak a.c.) it can withstand before the dielectric breaks down (it is often marked on it). 2. The leakage current: no dielectric is a perfect insulator but the loss of charge by leakage through it should be small.

Testing Capacitors