1. Energy Stored by Capacitors Last lesson we plotted the graph of Charge against voltage for a capacitor and learnt that the gradient of the graph represented theinof the capacitor. Capacitance Farads The graph was a straight line as shown below. Voltage (Volts) Charge (C) What does the area under this graph represent ? The area under a graph always represents... (quantity on ‘x’ axis  quantity on ‘y’ axis) So in this case it represents... Voltage  Charge But we already have a definition and a formula which tells us what this is A Volt is a...Joule per Coulombor So the area under the Charge/ Voltage graph represents the Energy stored by the capacitor.

2. Clearly the area is a triangle, so its area is given by the maths formula: Looking at the actual quantities represented by ‘Base’ and ‘Height’ This gives: or v This formula is useful if we know the charge stored, but we are much more likely to know the capacitance of the capacitor, so a second formula can be derived: or v

3. Experiment to show that Energy stored by capacitor is (approximately) proportional to V 2. Using the circuit shown, connect a large capacitor to a motor which has a pulley, string and mass attached to it as shown in the diagram. Bench MotorPulley String Mass 1. Connect the flying lead to point ‘X’ to charge the capacitor. 2. Move it to point ‘Y’ so that the capacitor discharges through the motor. The motor should lift the mass. 3. Repeat, and adjust the amount of mass until the weight almost touches the pulley. (If it flies around the top of the pulley and hits you in the face you have reduced the mass too much !) 4. Now charge the capacitor using one batteries instead of two. The weight should only rise to about a quarter of the height it did before. Conclusion : Half the voltage gave a quarter of the GPE. Teacher Note. Use large 25 000  F capacitors and 2 x 6v batterys in series and mass = 30g with larger motors (red pulleys) Circuit M XY ‘Flying’ lead Two 6 v batteries

4. Energy Stored by Capacitors Last lesson we plotted the graph of Charge against voltage for a capacitor and learnt that the gradient of the graph represented theinof the capacitor. The graph was a straight line as shown below. Voltage (Volts) Charge (C) What does the area under this graph represent ? The area under a graph always represents... So in this case it represents... But we already have a definition and a formula which tells us what this is A Volt is a...or So the area under the Charge/ Voltage graph represents

5. Clearly the area is a triangle, so its area is given by the maths formula: Looking at the actual quantities represented by ‘Base’ and ‘Height’ This gives: or This formula is useful if we know the charge stored, but we are much more likely to know the capacitance of the capacitor, so a second formula can be derived: or

6. Experiment to show that Energy stored by capacitor is (approximately) proportional to V 2. Using the circuit shown, connect a large capacitor to a motor which has a pulley, string and mass attached to it as shown in the diagram. Bench MotorPulley String Mass 1. Connect the flying lead to point ‘X’ to charge the capacitor. 2. Move it to point ‘Y’ so that the capacitor discharges through the motor. The motor should lift the mass. 3. Repeat, and adjust the amount of mass until the weight almost touches the pulley. (If it flies around the top of the pulley and hits you in the face you have reduced the mass too much !) 4. Now charge the capacitor using two cells instead of 4. The weight should only rise to about a quarter of the height it did before. Conclusion : Circuit M XY ‘Flying’ lead Four 6 v batteries

7. Questions Page 97