Warm Up: Determine the capacitance of a single capacitor that will have the same effect as the combination shown below. Each Capacitor has a Capacitance of 3F.

Warm Up (Without Numbers): Determine the capacitance of a single capacitor that will have the same effect as the combination shown below. C1=C2= C3=C

Energy stored in a capacitor The energy stored in a capacitor is the same as the work needed to build up the charge on the plates. As the charge increases, the harder it is to add more charge. Potential energy is the charge multiplied by the potential, and as the charge builds up the potential does too. If the potential difference between the two plates is V at the end of the process, and 0 at the start, the average potential is V / 2. Multiplying this average potential by the charge gives the potential energy : UC = ½Q V. Substituting in for Q, Q = CV, gives: The energy stored in a capacitor is: UC = ½C V2

If the distance between the plates of a capacitor is changed, the capacitance is changed. For a charged capacitor, a change in capacitance correspond to a change in voltage, which is easily measured. This is exploited in applications ranging from certain microphones to the the keys in some computer keyboards.

Capacitors “STORE” energy Anytime you have a situation where energy is “STORED” it is called POTENTIAL. In this case we have capacitor potential energy, Uc Suppose we plot a V vs. Q graph. If we wanted to find the AREA we would MULTIPLY the 2 variables according to the equation for Area. A = bh When we do this we get Area = VQ Let’s do a unit check! Voltage = Joules/Coulomb Charge = Coulombs Area = ENERGY

Potential Energy of a Capacitor Since the AREA under the line is a triangle, the ENERGY(area) =1/2VQ This energy or area is referred as the potential energy stored inside a capacitor. Note: The slope of the line is the inverse of the capacitance. most common forms