CAPACITANCEA capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

Parallel-plate capacitor connected to battery. (b) is a circuit diagram.CAPACITANCE

Consist of 2 parallel plate separated by a distance d

If connected to +ve and ve battery, electron are pulled of the one plates, leaving its with a charge of +Q

Electron then transfer through battery to the other plate leaving it with a charge of Q

This process stop when the potential different across the plates equal to potential different of the batteryCAPACITANCE

When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage:The quantity C is called the capacitance.Unit of capacitance: the farad (F)1 F = 1 C/VCAPACITANCE

The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor.For a parallel-plate capacitor:COMBINATION CAPACITANCE

Examplea) Calculate the capacitance of a parallel plate capacitor whose plates are 20 cm x 3.0 cm and are separated by 1.0 mm air gap. b) What is the charge on each plate if a 12 V battery is connected across the two plates?c) What is the electric field between plates?d) Estimate the area of the plates needed to achieve a capacitance of 1F with air gap, d= 1.0 mm.

Capacitance, C = 0 (A / d)Charge, Q = C VElectric field, E = V / d

a) Area , A = (20 x 10-2m)(3.0x10-2m) = 6.0 x 10-3 m C = 0 (A / d) = (9 x10-12) (6.0x10-3 / 1.0 x 10-3) = 53pF

b) Q = CV= (53x10-12)(12)= 6.4x10-10 C

c) E = V/d = (12 V ) / ( 1.0x10-3) = 1.2 x 104 V/m

d) C = 1.0 F , d = 1.0 mmA = Cd / 0 = (1 F ) ( 1.0 x 10-3) / (9x10-12) = 108 m2

Energy stored in charged capacitorA capacitor can store energyCharges stored can be discharged.If equipment uses high voltage, such as TV set, charges stored is big, hence high voltage presentUnplugging the TV set after usage does not make it safe to open the casing and touch the components inside !!

Starting with uncharged plates.When a charge is transferred form one plate to the other, pot. diff. exists between plates.Work must be done to move further charges thro this pot. diff.As more and more charges transferred, the pot. diff. increases, and more work required.

Storage of Electric EnergyA charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor.ExampleA camera flash unit stores energy in a 150F capacitor at 200 V. how much electric energy can be stored.

PE = CV2 = (150 x 10-6) (200)2 = 3.0 J

The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field:The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source be careful!Storage of Electric Energy

Combinations of capacitorsTwo or more capacitors are often combined in electric circuitsWe can calculate the equivalent of certain combinationsCircuit symbols for capacitors, batteries, and switches. Note that capacitors are in blue and batteries and switches are in red.

Parallel Combinations(a) A parallel combination of two capacitors in an electric circuit in which the potential difference across the battery terminals is V.

The individual potential differences across capacitors connected in parallel are the same and are equal to the potential difference applied across the combinationV = V1 = V2

The total charge on capacitors connected in parallel is the sum of the charges on the individual capacitorsQ = Q1 + Q2Where Q1 = C1V and Q2 = C2V

If we wish to replace the two capacitors with one equivalent capacitor having a capacitance CeqThe equivalent capacitor must store Q charge and has voltage VHence, Q = CeqVSubstituting into Q = Q1 + Q2 givesCeqV = C1V + C2V, thusCeq = C1 + C2If more than two capacitors in parallel,Ceq = C1 + C2 + C3 + .

Series CombinationWhen batteries connected, electrons transferred out of left plate C1 into right plate of C2Negative charge accumulate on the right plate of C2, equal amount of negative charge forced off the left plate of C2, hence left plate of C2 has excess of positive chargeNegative charge leaving left plate of C2 causes negative charge to accumulate right plate of C1.Hence all right plates end up with Q and all left plates end up with +Q

Charges on capacitors in series are the same.Q = Q1 = Q2and the total potential difference across any number of capacitors connected in series is the sum of the potential differences across the individual capacitors.V = V1 + V2

The equivalent capacitance can be calculated as follows:butfor each capacitor. Using the fact that V = V1 + V2 , hence

Hence for two or more capacitors joined in series

All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs)

Energy stored in a capacitorA camera flash

Heart defibrillators use electric discharge to jump-start the heart, and can save lives.Electric Energy Storage

Capacitors in parallel have the same voltage across each one. The equivalent capacitor is one that stores the same charge when connected to the same battery: Capacitors in Series and Parallel

Capacitors in series have the same charge. In this case, the equivalent capacitor has the same charge across the total voltage drop. Note that the formula is for the inverse of the capacitance and not the capacitance itself!Capacitors in Series and Parallel

Problem : QuestionFind the equivalent capacitance between a and b for the combination of capacitors shown in figure (a) below

Capacitor: nontouching conductors carrying equal and opposite charge. Capacitance: Capacitance of a parallel-plate capacitor:Summary

Capacitors in parallel:

Capacitors in series:Summary

Energy density in electric field:

A dielectric is an insulator. Dielectric constant gives ratio of total field to external field. For a parallel-plate capacitor:Summary

*Active Figure 26.9 (b) The circuit diagram for the parallel combination. *Active Figure 26.9 (c) The equivalent capacitance is Ceq C1=C2.

*Active Figure 26.10 (b) The circuit diagram for the series combination. *Active Figure 26.10 (c) The equivalent capacitance can be calculated from the relationship 1 /Ceq =1 /C 1+ 1/ C 2 .

*Fig 26-CO All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs)*Figure 24-14. Heart defibrillator.*Figure 24-9. Capacitors in parallel: Ceq = C1 + C2 + C3 .*Figure 24-10. Capacitors in series: 1/Ceq = 1/C1 + 1/C2 + 1/C3.*Figure 26.11 (Example 26.4) To find the equivalent capacitance of the capacitors in part (a), we reduce the various combinations in steps as indicated in parts (b), (c), and (d), using the series and parallel rules described in the text.