1 Boardworks A2 Physics Capacitors06/12/2017 Boardworks A2 Physics Capacitors 1

2 Boardworks A2 Physics Capacitors06/12/2017 Boardworks A2 Physics Capacitors Teacher notes In ‘Slide Show’ mode, click the name of a section to jump straight to that slide. 2

3 Discovery of the capacitor06/12/2017 Boardworks A2 Physics Capacitors Photo credit (von Kleist’s apparatus): SCIENCE PHOTO LIBRARY Leyden jar. Historical artwork of a man (at left) holding a Leyden jar, the earliest type of capacitor. A capacitor is a device for storing electric charge and the jar is storing electricity generated by the spherical electrostatic generator at right. The Leyden jar contains water and a brass rod. The man holding it acts as an earthed conductor. Now rarely used outside of the classroom, the Leyden jar was invented at the University of Leyden in the Netherlands in 1746. Photo credit (modern capacitors, top): © Shutterstock 2010, J and S Photography Photo credit (modern capacitors, bottom): © Shutterstock 2010, Adrio Communications Ltd

4 Capacitance and the farad06/12/2017 Boardworks A2 Physics Capacitors Capacitance is the ability of a body to hold an electric charge. It may also be described as the amount of electric charge for a given voltage. The standard unit for capacitance is the farad (F) named after Michael Faraday, who was the first to develop capacitors effective enough for practical applications, and to measure the effect of different variables on their capacitance. Teacher notes Faraday developed a ‘variable-dielectric’ capacitor, consisting of two half-spherical shells, between which he could place a range of different dielectric materials to investigate their effects. He was the first to try to use a capacitor to store charge in between experiments, treating it as a temporary power storage device. Photo credit: copyright expired One farad is the capacitance when 1 V voltage appears across a capacitor’s plates when a charge of 1C is stored. circuit symbol for a capacitor

5 Boardworks A2 Physics CapacitorsInside a capacitor 06/12/2017 Boardworks A2 Physics Capacitors 5

6 Do capacitors store charge or energy?06/12/2017 Boardworks A2 Physics Capacitors It is common to describe a capacitor as a circuit component that ‘stores charge’. What does this mean? When a capacitor is charged, electrons move off one plate and onto the other. What is the overall change in charge? uncharged charged The capacitor remains neutral. There is no net charge stored. However, the charge difference has created an electric field that is capable of moving (doing work on) any other charged particle that is placed between the capacitor plates. The capacitor stores electrical potential energy.

7 Investigating charge and voltage06/12/2017 Boardworks A2 Physics Capacitors Teacher notes Data collected in this virtual experiment can be used to plot a charge/voltage graph in the activity on the next slide. 7

8 Recording your results06/12/2017 Boardworks A2 Physics Capacitors Teacher notes The gradient of the graph represents the ability of the capacitor to store charge: the steeper the graph, the more charge it stores for a given voltage. This is the capacitance as defined on slide 4. 8

9 The capacitor equation06/12/2017 Boardworks A2 Physics Capacitors 9

10 Factors affecting capacitance06/12/2017 Boardworks A2 Physics Capacitors What factors determine the capacitance of a capacitor? area – The greater the area of the plates, the more charge can be stored for a particular voltage. Capacitance is proportional to area. distance – The greater the space between the plates, the less effect they have on each other, so the capacitance is reduced. Capacitance is inversely proportional to distance. permittivity – The higher the permittivity of the dielectric, the greater its ability to transmit an electric field between the plates, and the higher the capacitance. Capacitance is proportional to permittivity. C = ε A d 10

11 Capacitors in parallel06/12/2017 Boardworks A2 Physics Capacitors If a capacitor has a capacitance of 10 µF, what is the capacitance of two identical capacitors connected in parallel? Adding a second capacitor in parallel increases the area for charge storage. This increases the capacitance. 10 µF The individual values of capacitance for n parallel capacitors can be added to obtain a single value, CT: 10 µF CT = C1 + C2 + … + Cn 20 µF This is the equivalent capacitance. Replacing parallel capacitors in a circuit with a single capacitor of the same total capacitance does not affect the rest of the circuit.

12 Boardworks A2 Physics CapacitorsCapacitors in series 06/12/2017 Boardworks A2 Physics Capacitors If a capacitor has a capacitance of 10 µF, what is the capacitance of two identical capacitors connected in series? Adding a second capacitor in series increases the effective distance between the positive and negative plates (charges on the plates in the middle cancel to zero). This decreases the capacitance. d 10 µF 10 µF The equivalent capacitance, CT, is given by: 2d CT 1 C1 C2 Cn = + + … + 5 µF So the capacitance of two 10 µF capacitors in series is 5 µF. 12

13 Equivalent capacitance – calculations06/12/2017 Boardworks A2 Physics Capacitors 13

14 Boardworks A2 Physics CapacitorsCapacitance summary 06/12/2017 Boardworks A2 Physics Capacitors 14

15 Boardworks A2 Physics Capacitors06/12/2017 Boardworks A2 Physics Capacitors Teacher notes In ‘Slide Show’ mode, click the name of a section to jump straight to that slide. 15

16 Discharging a capacitor06/12/2017 Boardworks A2 Physics Capacitors A 200 µF capacitor is charged to 10 V, then discharged through a 250 kΩ resistor. A data logger records the voltage across the capacitor at 10 s intervals for 90 s. time / s voltage / V 10.0 8.2 3.7 3.0 2.5 1.7 2.0 10 20 30 40 50 60 70 80 90 6.7 5.5 4.5 Teacher notes A data logger is a device that takes measurements at regular, accurate intervals. The voltage across a capacitor changes continuously as it is discharged, making it hard to record accurately using only a voltmeter. This data can be plotted on a graph using the activity on the next slide. How would you expect the results to look? 16

17 Plotting a discharge curve06/12/2017 Boardworks A2 Physics Capacitors 17

18 Boardworks A2 Physics CapacitorsThe time constant – RC 06/12/2017 Boardworks A2 Physics Capacitors A capacitor C discharges through a resistor R when a switch is closed. The time taken for the capacitor to discharge depends on both R and C. R C The product of R and C is called the time constant for the circuit, and gives an indication of how long the capacitor takes to discharge. What are the units of the time constant, RC? F × Ω = C / V × V / A [using equations Q = C V and V = I R] = C / A = A × s / A [charge = current × time] = s 18

19 Changing the discharge time06/12/2017 Boardworks A2 Physics Capacitors 19

20 Capacitor decay equation06/12/2017 Boardworks A2 Physics Capacitors This is the equation for the exponential decay curve: V = V0 e–(t / RC) How can we rearrange this equation to calculate t, or RC? An exponential equation is the same as any other – when rearranging it, always do the same to both sides. The inverse (or opposite) of e is the natural logarithm, written ‘ln’ and found on your calculator: V / V0 = e–(t / RC) ln (V / V0) = –t / RC t = –RC ln (V / V0) RC = –t / ln (V / V0) 20

21 How does charge change with time?06/12/2017 Boardworks A2 Physics Capacitors If the voltage of a discharging capacitor drops off at a rate of V = V0 e–(t / RC), what happens to the charge on its plates? What equation relates the voltage and charge of a capacitor? Q = C V The capacitance, C, is a fixed property of the capacitor, so this is a constant. Substitute the equation for V: Q = C V0 e–(t / RC) At time 0, Q0 = C V0, so the equation can be simplified to: Q = Q0 e–(t / RC) 21

22 How does current change with time?06/12/2017 Boardworks A2 Physics Capacitors As a capacitor discharges, voltage and charge drop exponentially. What happens to the current in the circuit? Current is equal to the charge passing a fixed point per second. It is the same at every point in the circuit. When the capacitor starts discharging, the charge drops quickly so the current is high. As the capacitor discharges, the charge drops more slowly so the current drops too, until the charges on the plates are balanced again and the current is zero. using V = I R: I = V / R = V0 e–(t / RC) / R using V0 = I0 R I = I0 e–(t / RC)

23 Other forms of exponential decay06/12/2017 Boardworks A2 Physics Capacitors Capacitor discharge Radioactive decay Initial charge Q0 Initial parent nuclei N0 Q = Q0 e–(t / RC) N = N0 e–(λ t) RC = time to fall to Q0 / e Half life (t½) = time to halve Charge, current and voltage all exponentials Number and activity both exponential V0 A0 voltage activity RC t½ time time

24 Discharging a capacitor – calculations06/12/2017 Boardworks A2 Physics Capacitors

25 Boardworks A2 Physics Capacitors06/12/2017 Boardworks A2 Physics Capacitors Teacher notes In ‘Slide Show’ mode, click the name of a section to jump straight to that slide. 25

26 What makes capacitors useful?06/12/2017 Boardworks A2 Physics Capacitors Capacitors store electrical potential energy. The use of this energy as a power source is one of their main applications. The energy can be released quickly or slowly, depending on the resistance of the discharge circuit. If a capacitor is discharged quickly through a low resistance circuit, it produces a short burst of large current. This is how a camera flash is powered. Photo credit: © Shutterstock 2010, Murat Baysan If a capacitor is discharged slowly through a high resistance circuit, it produces a low current over a longer time. This can be useful as a temporary power supply, such as to power the internal memory of a device while its batteries are changed.

27 Capacitors as energy sources06/12/2017 Boardworks A2 Physics Capacitors 27

28 Energy transfer in a defibrillator06/12/2017 Boardworks A2 Physics Capacitors

29 Energy stored in a capacitor06/12/2017 Boardworks A2 Physics Capacitors A capacitor is charged up to 5 V. This means it stores 5 J of potential energy per coulomb of charge. When the capacitor is discharged, its voltage starts to drop, but if it is only discharged by a small amount, then the energy released is 5 JC–1. This is equal to the area of a small strip on the Q-V graph: The voltage is now lower, so if it is discharged by another small amount, the energy released is equal to the next small strip, etc. Q charge The total energy stored is equal to the sum of all these strips, or the area under the graph: voltage V W = ½ Q V 29

30 Energy storage equation06/12/2017 Boardworks A2 Physics Capacitors 30

31 Alternative energy storage equations06/12/2017 Boardworks A2 Physics Capacitors The equation W = ½ Q V gives the energy stored when a charge Q is stored on a capacitor at voltage V. How can the energy stored be calculated if only the capacitance and the voltage are known? Can you think of an equation that links charge, capacitance and voltage? Q = C V the capacitor equation: Substitute this into the energy equation to find a new formula for W: W = ½ Q V = ½ C V × V W = ½ C V 2 Can you find an equation for W in terms of only Q and C? W = ½ Q2 / C 31

32 Energy storage: true or false?06/12/2017 Boardworks A2 Physics Capacitors 32

33 Boardworks A2 Physics Capacitors06/12/2017 Boardworks A2 Physics Capacitors Teacher notes In ‘Slide Show’ mode, click the name of a section to jump straight to that slide. 33

34 Boardworks A2 Physics CapacitorsGlossary 06/12/2017 Boardworks A2 Physics Capacitors Teacher notes capacitance – The ability of a body to store or separate charges so as to produce an electrical potential. capacitor – A device that stores energy in an electric field between two conductors. coulomb – The SI unit of electrical charge. coulomb meter – A device for measuring charge. defibrillator – A device that uses a powerful electric current to stop a fluttering heart for a moment, so that it can restart with its natural rhythm. dielectric – A material that does not transmit an electric current. A non-conductor. equivalent capacitance – The capacitance of a single capacitor that would be equivalent to any combination of capacitors in series or parallel. exponential decay – Describes a quantity that drops at a rate proportional to its value. Examples include the voltage, charge and current of a discharging capacitor, and radioactive decay. permittivity – A measure of a material’s ability to transmit (or ‘permit’) an electric field. time constant – In a discharging or charging circuit, the time constant is given by the product of the resistance and capacitance in the circuit (RC). Measured in seconds it is how long charge, current and voltage all take to fall to 1/e of their initial values. 34

35 Boardworks A2 Physics CapacitorsWhat’s the keyword? 06/12/2017 Boardworks A2 Physics Capacitors 35

36 Boardworks A2 Physics CapacitorsMultiple-choice quiz 06/12/2017 Boardworks A2 Physics Capacitors 36