Capacitance What do you expect to happen when you close the switch? Actually nothing doesn’t happen - as you well know, one wire “becomes positive and the other negative”. This is caused by a deficit of electrons on the left and a surplus on the right. The current flow to achieve this is tiny BUT if we set up conditions correctly, we can make it big enough to measure.

AA Two large metal plates very close together but not touching. Close the switch and a tiny current flows - the capacitor is charged. Remove the cell from the circuit and then close the switch again and a tiny current flows back the other way - the capacitor discharges. This can be shown with the demo capacitor and a bulb. Capacitors  store charge  do not pass a continuous dc  can pass current by constantly charging and discharging - ac

The charge distribution is not part of the symbol, but note that the charge resides inside the plates of the capacitor and should always be drawn there if needed. Capacitance This is a measure of how much charge a capacitor can store per unit potential difference across it “how many coulombs you get for your volts” The total charge remains equal it is just redistributed. Circuit Diagram Title links to a website applet to show this AA

The area under the curve (in units of As) is equal to the charge stored in the capacitor. A plot of current vs time gives: This curve is an exponential curve following all the rules of a half life curve.  (Time Constant = CR) 37%I max I=V/R I/A t/s (0,0) Note that theoretically it never reaches the I = 0 line - your examiner will expect it not to when you sketch it.

You should remember that I = dQ/ dt so ie Q = area under curve

C = Q / V or Q = CV unit of capacitance is the farad (F). The unit of capacitance is the farad (F). It is a very large unit. You will more often meet the following  F = 1x10 -6 F nF = 1x10 -9 F pF = 1x F What applied voltage would charge a 1  F capacitor to 1.0x10 -5 C. V = Q / C V = 1.0x10 -5 C / 1x10 -6 F V = 10V If a graph of charge stored against voltage is plotted you get a straight line through the origin. The constant of proportionality is the Capacitance, defined as follows. Capacitance = Charge stored Voltage applied

Another method of finding the capacitance is to change the resistance in series with the capacitor and therefore control the discharging current. If the resistance is decreased as the capacitor discharges you can keep the current constant until the capacitor is fully discharged. The current time graph then looks more like this. Time Current Conduct the experiment as described on the sheet to verify this theory!experiment

Charging a capacitor Maximum current  Occurs initially  Q = 0 so V c = 0 so V R = V  I max = V/R Maximum voltage  Initially across Resistor V battery = V resistor  This will fall as Voltage across Capacitor increases V battery = V capacitor + V resistor  So finally the maximum Voltage will be across Capacitor  When V battery = V capacitor Maximum Charge  After some time  Q = CV AA R V C

Conduct the experiment as described on the practical sheet and record your results using Insight so that you can calculate the areas under the graphs. The voltage across the resistor can be used to calculate the current! Its takes longer to charge a larger capacitor through a larger resistor. Why?? Because less charge is pushed through per second or more of the voltage is used up by the resistor!

Using the set up as for charging a capacitor, you should now discharge it and log the current flowing every 5 secs with the circuit as shown. The resistance should then be changed from 80K to 40K and 20K (or similar), using the variable resistor and the multi-meter to check the values. Plotting a graph of current against time should show the effects of the resistance changing. Effect of resistance

Since Q = CV And V = IR therefore I = Q/CR If the capacitor is fully charged each time, Q is a constant. High Resistance Medium Resistance Low Resistance If the same capacitor is used C is a constant. Therefore I  1/R This will produce graphs like….

Energy stored If we plot a graph to show how the pd changes across a capacitor with a charge Q stored on it we get – This shows that the capacitance of a capacitor does not depend on pd – it is constant.

This graph also enables us to calculate the energy stored on the capacitor - As the charge on the capacitor increases, so extra work needs to be done to add more charge. This means that the area under the line gives us the work done and therefore the energy stored.

Work done to charge = energy stored = area under graph = ½ QV Combining this with Q=CV we get..... W= ½ QV = ½ CV 2 = Q 2 /2C