N.ShubadharshiniII B.sc Physics 13UPHY032 CAPACITANCE OF A CAPACITOR

Capacitance What are capacitors?What do we use them for (in real life)What do we want to know about a capacitor:CapacitanceChargePotentialStored energyConnection with other capacitorsFilling with dielectrics

25-1: The use of capacitors:

Store electric (potential) energy (e.g. photoflash unit (slow build-up, rapid release)

Tuning radio (or TV) transmitters and receivers

Store data in computers

25-2: Capacitance (C):C = Q/VWhat is Q, V and C?What does it mean for a capacitor to have a big C?How does the parallel plate capacitor look like?What is the net charge on a capacitor?What does C depend on?Does C depend on Q or V?

Charging a capacitor:A battery is a device that maintains a certain potential difference between its (positive and negative) terminals. What is the schematic symbol for capacitor? What do we call the SI units of capacitance?Is one farad big or small? Very big!The circuit is incomplete when the electric switch is open.Checkpoint 1: What happens to the capacitance of a capacitor when the charge on each the two conductors double?

25-3: Calculating the capacitance Method: Put charge Q and Q, calculate E, and from it calculate V (i.e. DV), divide Q/V to get C.For parallel plate capacitor: C = eo A/dFor cylindrical capacitor:C = 2p eo (L/ln[b/a])

For an isolated sphere of radius R, b C = 4p eo RCheckpoint-2: A 10-volt battery charges a capacitor. What can you say about the charge stored on each of the conductors of the capacitor when (a) the distance between the parallel plates increases? (b) the radius of the inner cylinder decreases? (c) the radius of the outer sphere increases?For spherical capacitor [inner radius a, out radius b, air (or vacuum) in between]C = 4p eo (a b/[b-a])

25-4: Capacitors in parallel and in series: 1- In parallel: The voltage is the same across the capacitors.Ceq = CiExample: In the two circuits of this slide, assume the battery is 9 volts, and that C1 = 2 C2 = 3 C3 = 3 mF. What can you say about the voltages across and the charges each of the six capacitors?2- In series: The charge is the same on the capacitors.Ceq-1 = (Ci) -1

25-5: Energy stored in an electric field: How much work must be done to charge an initially uncharge capacitor to a charge Q?One can prove [pg. 600] that for a parallel plate capacitor, the electric energy per unit volume [called the energy density (u or ue)] is: ue = eo E2Interaction: prove this!dW = V dqW = Q2/C = C V2 = Q VExample: what is the energy stored in a 20 nF parallel plate capacitor when it is charged to 50 volts?This is true even for non parallel plate capacitors

25-6: Capacitors with a dielectric:

C = k CoBattery is connected: Q = k Qo ; V = Vo; U = k UoBattery not connected:Q = Qo ; V = Vo/k ; U = Uo/k

*Q = C V, V is constant(a) decrease, (b) increase, (c) decrease*25 micro-joule