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Chapter 25: Capacitance

Chapter 25: Capacitance. Intro: What are we going to talk about in chapter 26:. What are “ capacitor ” s? What do we use them for (in real life) What do we want to know about a capacitor: Capacitance Charge Potential Stored energy Connection with other capacitors

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Chapter 25: Capacitance

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  1. Chapter 25: Capacitance Intro: What are we going to talk about in chapter 26: • What are “capacitor”s? • What do we use them for (in real life) • What do we want to know about a capacitor: • Capacitance • Charge • Potential • Stored energy • Connection with other capacitors • Filling with dielectrics

  2. 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

  3. 25-2: Capacitance (C): C = Q/V What is Q, V and C? What is the net charge on a capacitor? What does it mean for a capacitor to have a big C? Does C depend on Q or V? What does C depend on? How does the parallel plate capacitor look like?

  4. What is the schematic symbol for capacitor? What do we call the SI units of capacitance? Is one farad big or small? Very big! Charging a capacitor: A battery is a device that maintains a certain potential difference between its (positive and negative) terminals. 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?

  5. 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/d For cylindrical capacitor: C = 2peo (L/ln[b/a])

  6. For spherical capacitor [inner radius a, out radius b, air (or vacuum) in between] C = 4peo (a b/[b-a]) For an isolated sphere of radius R, b → ∞ C = 4peo R Checkpoint-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?

  7. 25-4: Capacitors in parallel and in series: 1- In parallel: The voltage is the same across the capacitors. Ceq = ΣCi 2- In series: The charge is the same on the capacitors. Ceq-1 = Σ(Ci) -1 Example: 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?

  8. 25-5: Energy stored in an electric field: How much work must be done to charge an initially uncharge capacitor to a charge Q? dW = V dq W = ½ Q2/C = ½ C V2 = ½ Q V 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 = ½eo E2 Interaction: prove this! This is true even for non parallel plate capacitors Example: what is the energy stored in a 20 nF parallel plate capacitor when it is charged to 50 volts?

  9. 25-6: Capacitors with a dielectric: C = k Co Battery is connected: Q = k Qo ; V = Vo; U = k Uo Battery not connected: Q = Qo ; V = Vo/k ; U = Uo/k

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