LECTURE 19 CAPACITORS. Instructor: Kazumi Tolich

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1 LECTURE 19 CAPACITORS Instructor: Kazumi Tolich

2 Lecture 19 2! Reading chapter 20-5 to 20-6.! Capacitance! Parallel-plate capacitor! The storage of electrical energy! Dielectrics

3 Capacitors 3!!!!! A capacitor is a device consisting of two conductors. One conductor with charge Q, and the other with charge -Q will have a potential difference between them. The size of the potential difference between two conductors of a capacitor depends on the shape and orientation of the two conductors. Capacitors are used in variety of electronics devices. The symbol for a capacitor in a circuit diagram is

4 Capacitance 4! The capacitance of the capacitor is a property of the geometry of the objects and defined as C = Q V! Capacitance is a measure of the capacity to store charge for a given potential difference.! Since V is proportional to Q, C does not depend on either Q or V.! The SI unit of capacitance is the farad (F), which is equivalent to the (C/V).

5 5 Clicker question: 1 & 2

6 Example: 1 6! A storage capacitor on a random access memory (RAM) chip has a capacitance of C = 55 ff. If the capacitor is charged to V = 5.3V, how many excess electrons are on its negative plate?

7 Parallel plate capacitor 7! A common capacitor geometry is the parallel-plate capacitor.! In a parallel-plate capacitor, two plates of conductors are closely placed parallel to each other.! The separation of the plates is much smaller than the length and width of the plates.

8 E of a parallel plate capacitor 8! If a charge +Q is placed on one plate, and Q on the other, they will be distributed evenly on the inner surfaces of the plates with area, A. The separation of the plates is d.! The E field between the plates is uniform and given by E = Q ε 0 A! The potential difference between the plates is given by ΔV = Qd ε 0 A

9 Capacitance of a parallel plate capacitor 9! The capacitance of a parallel plate capacitor is C = ε 0A d! Note that the capacitor depends only on the geometry, the area, A, and the separation, d.! The capacitance increases as the plates become larger and decreases as the separation increases. This is a general trend in all capacitors.

10 Demo: 1 10! Variable capacitor! Tuning capacitor used in AM radios, in which the overlapping area between the plates can be changed. C = Q V = ε 0 A d V 1 A

11 Example: 2 11! Two sheets of aluminum foil have the same area, a separation of d = 1.00 mm, and a capacitance of C = 10. pf, and are charged to V = 12 V. a) Calculate the area of each sheet, A.! Now, the separation is decreased by 0.10 mm with the charge held constant. b) What is the new capacitance? c) By how much does the potential difference change?

12 Key board 12! There is a capacitor under each key.! As you press a key, the spacing between the capacitor plates change, increasing the capacitance. C = Q V = ε 0A d

13 Condenser microphones 13! In a condenser microphone, also called a capacitor microphone or electrostatic microphone, the diaphragm acts as one plate of a parallel-plate capacitor.! The sound (vibrations of air) produces changes in the distance between the plates. C = Q V = ε 0A d

14 Electrical potential energy in capacitors 14! A charged capacitor stores electrical potential energy.! The energy stored is the total amount of energy required to charge the plates by moving increments of charge, ΔQ, from one plate to the other. U = QV av! Since C = Q/V, the energy stored in a capacitor is given by U = 1 2 QV = 1 2 Q 2 C = 1 2 CV 2

15 Electrostatic field energy 15! The energy stored in a capacitor can be thought as energy stored in the electric filed, electrostatic field energy.! The energy density u E stored in any electric field is u E = energy volume = 1 2 ε 0 E 2

16 Camera flash and electronics 16! A capacitor can store a large amount of charge.! A flash unit of a camera uses a large amount of charge in a short amount of time.! In most electronics boards, we use capacitors where we need to use a lot of charge quickly.

17 Defibrillator 17! A jolt of electric current from a defibrillator can restore normal heartbeat.! A capacitor is used to store a large amount of charge (and energy).! The charged capacitor is discharged quickly to deliver the charge and the energy to a person in distress.

18 Demo: 2 18! Capacitor energy! Three 1500 mf capacitors connected in parallel are charged to 400 volts.! Capacitors store energy and could be dangerous. U = 1 2 CV 2 = 1 ( F) ( 400V) 2 = J

19 Dielectrics 19! A non-conducting material is called a dielectric.! If we place a dielectric material between the plates of a capacitor, molecules within can be polarized.! The dipoles rotate and align with the E field from the plates.

20 Dielectrics: 2 20! This creates surface charge (bound charges) on the dielectric faces near the plates.! The bound charge creates an electric field pointing in the opposite direction.

21 E and V of a capacitor with a dielectric 21! If the capacitor is isolated (not connected to a battery), the total electric field between the plates is reduced due to a dielectric material. E = E 0 κ where E 0 is the electric field without the dielectric, and κ is the dielectric constant.! Since the E field strength is reduced, the potential difference between the plates is also reduced. V = Ed = E 0d κ = V 0 κ where V 0 is the potential difference without the dielectric.

22 Dielectric constants 22! The dielectric constant is a property of the material.! κ of air is very close to 1 (close to vacuum).

23 Is the battery connected? 23! The potential difference between the capacitor plates decreases as a dielectric is inserted only if the capacitor is isolated (not connected to a battery), and the total charge on the plates is not changing.! If a battery is connected, the potential difference between the plates remains the same as the terminal voltage of the battery.

24 Capacitance of a capacitor with a dielectric 24! The capacitance with a dielectric installed is increased and given by C = κc 0 where C 0 is the capacitance without any dielectric.! The capacitance of a parallel-plate capacitor with a dielectric is also increased. C = κ ε 0A d

25 Demo: 3 25! Parallel plate capacitor with dielectrics! Observation of the distance dependence of the capacitance. V = Q C = Q d ε 0 A! Observation of change in potential difference across a capacitor as a dielectric material is inserted in the parallel plate capacitor. V = V 0 κ

26 Example: 3 26! A parallel-plate capacitor is constructed with circular plates of radius r = m. The plates are separated by d = 0.25 mm, and the space between the plates is filled with a dielectric with dielectric constant κ. When the charge on the capacitor is Q = 1.2 µc, the potential difference between the plates is V = 750 V. Find the value of κ.

27 Stud finder 27! A stud finder has a capacitor with its plates arranged side by side.! When the device is moved over a stud, the capacitance increases since the stud acts as a dielectric material.! The device detects this change in capacitance.

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b to 2Q, while keeping the conductors in the same positions.