Higher Physics Unit 2 2.3 Capacitance
The Capacitor A capacitor consists of two metal plates, with an insulator in between. The circuit symbol for a capacitor is: A capacitor stores charge.
Charging A Capacitor An uncharged capacitor, is connected to a battery. + - + + - - Electrons flow from the negative terminal of the battery to one side of the capacitor. Electrons leave the other side of the capacitor and flow to the positive terminal of the battery. No current passes through the insulator, although there is a current in the circuit.
+ - Eventually, no more electrons can flow onto the capacitor, as negative repels negative. + + - - The capacitor is fully charged. No more current flows around the circuit. potential difference between the plates = supply voltage + + - - Disconnect the capacitor from the battery. The capacitor remains fully charged.
+ - + - Connect the charged capacitor to a lamp. All the electrons move off the plate, and flow towards positive. The bulb lights momentarily. The bulb goes off after a short time and stays off. The capacitor has fully discharged.
Capacitor Relationship Relationship between Q and V for a Capacitor The charge (Q) in a capacitor is measured using a coulombmeter, while the voltage across it is measured with a voltmeter. V C
Results Charge (nc) Voltage (V)
Graph The results are plotted as a graph. charge/nc Q V Q C V C Q V voltage/v capacitance (F) C Q V charge (C) potential difference (V)
Capacitance The unit of capacitance is FARADS (F). An alternative unit is coulombs per volt (C V -1 ). 1 F 1 C V 1 1 farad = 1 coulomb per volt
The farad is an exceptionally large unit, so most practical capacitors are measured in: microfarads (μ) = nanofarads (n) = picofarads (p) = 10 10 10 9 12 6 Example 1 A 220μF capacitor is connected to a 12 V battery. Calculate the maximum charge this capacitor is able to store. C V Q 220 μf 220 10 12 V? -6 F Q Q C V 220 2.64 10 10 6 3 12 C
Example 2 A capacitor connected to a 12 V battery stores 7.2 x 10-4 C of charge. (a) (b) Calculate the capacitance of the capacitor. If the capacitor discharges in 3 ms, calculate the size of the current flowing. (a) Q V C 7.2 12 V? 10 4 C C Q V 7.2 10 12 4 C 6 10 5 F
(b) Q 7.2 10 4 C Q I t t I 3 ms 3? 10-3 s I Q t 7.2 3 10 10-3 4 I 0.24A
Worksheet Electricity & Electronics Tutorial Page 13 Q7 Q12
Energy Stored in a Capacitor A graph of charge against voltage for a capacitor looks like this: charge/nc energy stored in C area under graph voltage/v E charge 1 2 Q V 1 energy (J) E 1 2 Q V (C) potential difference (V)
But if we substitute Q C V into equation 1: E 1 2 Q V E 1 2 C V V E 1 2 2 C V 2 capacitance energy (J) E 1 2 2 C V (F) potential difference (V)
Q But if we substitute V into equation 1: C E 1 2 Q V E 1 2 Q Q C E 1 2 Q C 2 3 charge (C) energy (J) E 1 2 Q C 2 capacitance (F)
Example 1 A 470 μf capacitor is charged to 12 V. Calculate the energy stored by the capacitor. C V E 470 μf 470 10 12 V? -6 F E E 1 2 1 2 2 C V 470 0.034J 10-6 12 2
Worksheet Electricity & Electronics Tutorial Page 14 Q13 Q14
Current in a Charging Capacitor An uncharged 1000 μf capacitor is connected as shown. 6 V S A 1000 μf 22 kω Switch S is closed and the current is measured every 5 seconds.
Results Time (s) Current (A)
Graph The results are plotted as a graph. I MAX current/a 0 time/s Extension Repeat the experiment using a 10 kω resistor.
Changing C big C current/a I MAX medium C small C time/s Why is the initial charging current always the same? Current is dependent on resistance which is unchanged in circuit.
Changing R current/a I MAX (small R) big R medium R small R I MAX (medium R) I MAX (big R) Why is the initial charging current different? time/s Current dependent on resistance. Small resistance => LARGE current.
Voltage Across Charging Capacitor Experiment An uncharged 1000 μf capacitor is connected as shown. 6 V S 1000 μf V 22 kω Switch S is closed and the potential difference is measured every 5 seconds.
Results Time (s) Potential Difference (V)
Graph The results are plotted as a graph. V MAX V MAX = emf potential difference/v time/s Extension Repeat the experiment using a 10 kω resistor.
Changing C V MAX potential difference/v big C medium C small C Why is the potential difference across C always the same? Supply voltage is unchanged. time/s
Changing R V MAX potential difference/v big R medium R small R time/s Why does a larger resistance result in the capacitor taking longer to charge? Large resistance gives small current, so capacitor takes longer to charge.
Charging Capacitors 6 V S 1500 μf V C 5 kω The maximum current occurs at the start of charging, just after closing switch S. R 5000Ω I MAX V R V I MAX 6V? I MAX 6 5000 1.2 10 3 A
The voltage across the capacitor cannot exceed the supply voltage. Graphs of current against time and voltage against time are shown. 1.2 current/ma 0 time/s potential difference across capacitor/v 6 0 time/s
Worksheet Electricity & Electronics Tutorial Page 14 Q15 Q17
Charging and Discharging X Y 9 V 5 kω V A The switch is set to X and then to Y. When the switch is set to X, the capacitor charges. The current is at its maximum value just when the switch is set to X. When set to Y, the capacitor discharges. When the size of R is increased, the maximum charging current decreases.
Graph of Current Against Time The capacitor was allowed to fully charge and discharge. current/ma I MAX time/s I MAX I MAX V R 9 5000 1.8 ma Graph of pd Against Time potential difference across capacitor/v V MAX time/s V MAX V S V MAX 9 V
1.8 current/ ma 0 20 30 50 60 65 70 time/s - 1.8 9 voltage across capacitor /V 0 20 30 50 60 65 70 time/s
Time (s) Description 0-20 Capacitor charges up fully 20-30 Capacitor remains fully charged 30-50 Capacitor discharges fully 50-60 Capacitor remains fully discharged 60-65 Capacitor partially charges 65-70 Partially charged capacitor fully discharges
Worksheet Electricity & Electronics Tutorial Page 16 Q18 Q19
Resistors and AC A resistor is connected to an AC voltage supply as shown. R A As the frequency of the AC voltage is increased, the current in the circuit is unchanged. A graph of current against frequency in a resistor circuit is: current/a frequency/hz
Capacitors and AC A capacitor is connected to an AC supply. V current/a As the frequency of the power supply is increased, the current increases. C A frequency/hz The current in the capacitor is directly proportional to the frequency.
Worksheet Electricity & Electronics Tutorial Page 16 Q20 Q23
Uses of Capacitors Blocking dc Transmitting ac V An electrical signal containing an ac and dc component. V dc V ac t This signal is input to the RC circuit shown. (an RC circuit is a circuit containing only a resistor and capacitor) V C R V R
The signal shown is the voltage variation across resistor R. V It no longer includes the dc component. V ac t Capacitors block dc.
Storing Charge Flash Lamp A flash lamp and capacitor are connected as shown. S 1 C R When switch S 1 is closed, the capacitor charges up. S 2 Once fully charged, close switch S 2 and a burst of light is seen. flash lamp The capacitor is discharging through the flash lamp.
Smoothing ac to dc V R An ac input is shown. t The ac from the supply is changed to dc by passing through a diode. (current flow in only one direction) V R V R An unsmoothed dc signal is achieved. t
Including capacitor C in the circuit as shown, smoothes the output. C V R The capacitor discharges at the zero parts. This output is called a ripple voltage. V R t
V R V R