1. Engineering Science EAB_S_127 Electricity Chapter 4

2. Introduction  Capacitance  Energy stored in a capacitor  Charging and Discharging through a resistor  Time constants

3. Capacitance  Capacitors are devices which store electrical charge  A capacitor consists of two plates separated by an insulator, as shown in Figure 4.1  The negative plate is connected to a low potential and the positive plate to a high potential Figure 4.1 Q V + + + - - - Positive plate Negative plate Insulator

4. Capacitance continued  The total amount of the charge stored, is denoted by Q and the voltage across the plates by V  The capacitance then is defined as  Where C is in Farads  1 Farad = 1 Coulomb per Volt Figure 4.1 Q V + + + - - - Positive plate Negative plate Insulator

5. Energy Stored in a Capacitor  When charged, a capacitor stores electrical energy  Recall the formula for electrical energy in a circuit, which is W = VQ  However, we need to be careful as the voltage between the plates in a capacitor varies from 0 to V  Hence, to be more accurate we should use the average voltage  Soand we know  Hence

6. Energy Stored in a Capacitor: Example  Question: A capacitor is supplied with 10 V in a circuit. If its capacitance is 150µF, what is the electrical energy stored in the capacitor?  Answer:

7. Charging and Discharging a Capacitor  Charging and discharging a capacitor from a DC (direct current) source is shown below  We assume that the voltage source, V, has no internal resistance  If the switch was held in position 2 for a long time, then the capacitor would be completely discharged, V c = 0V V

8. Charging a Capacitor  If the switch is then moved to position 1, current will start to flow through the resistor R, thereby charging the capacitor, C  The voltage across the plates of the capacitor will rise in time, until after a long time, the capacitor will have the same voltage as the supply, V V VCVC

9. Discharging a Capacitor  If the switch is then moved back to position 2, current will start to flow through the resistor R, thereby discharging the capacitor, C  The voltage across the plates of the capacitor will fall in time, until after a long time, the capacitor will have no charge at all and again, V c = 0V V VCVC

10. Time Constant of an RC Circuit  It can be shown mathematically, that the time for the voltage to fall to 37% of its original voltage,  = RC  The charging and discharging curves have an exponential nature  When discharging  When charging VCVC VCVC

11. RC Time Constant: Example  Question: If R = 1000  and C = 0.1  F, what is the time constant of the circuit?  Answer:  = RC = 1000x0.1x10 -6 = 0.1 x10 -3 = 100  s  Hence, when discharging, the following equation can be used to calculate the voltage  When charging

12. Summary  Learning Outcomes:  Capacitors and capacitance  Energy stored in a capacitor  Charging a capacitor  Time constants  Exponential charging and discharging curves