PHYSICS - CLUTCH CH 24: CAPACITORS & DIELECTRICS.

Transcription

1 !!

2 CONCEPT: CAPACITORS AND CAPACITANCE A CAPACITOR is formed by two surfaces of equal/opposite charge brought close together - Separation of charge potential energy stored Connecting a capacitor to a battery produces a simple CIRCUIT - Motivation for charges to move comes from a - A BATTERY is a good provider Whenever a SINGLE capacitor is connected to a SINGLE battery: - Voltage of battery voltage of capacitor - CHARGE on capacitor Q = CV CAPACITANCE measures the Larger the capacitance, the [ LARGER / SMALLER ] the charge stored CAPACITANCE is defined as C = - Units are F (Farads) EXAMPLE: What is the charge on the capacitor in the following figure? 9 V 3 F Page 2

3 CONCEPT: PARALLEL PLATE CAPACITORS Capacitance for ANY Capacitor is C = Q / V Capacitance for a PARALLEL PLATE Capacitor is C = - Where A is area, d is distance between plates, ε F m Remember: - Electric Field BETWEEN plates is. - Electric Field OUTSIDE plates is. - The magnitude of the UNIFORM Field is Equipotential surfaces between plates: +Q -Q EXAMPLE: A parallel plate capacitor has an area of 5 cm 2, a plate separation of 10 mm, and a voltage across the plates of 100 V. What is the charge of the capacitor? Page 3

4 PRACTICE: CAPACITANCE OF PARALLEL CIRCULAR PLATES Two circular plates of radius 2cm are brought together so their separation is 5mm. What is the capacitance of these plates? EXAMPLE: POINT CHARGE IN CAPACITOR Two 1 cm by 1 cm plates, separated by 10 mm, form a capacitor. If each plate is charged to 30 nc, (a) What is the potential difference between the plates? (b) What is the electric field between the plates? (c) How much energy does it take to move a 5 nc charge from the positive plate to the negative plate? PRACTICE: CHARGING A CAPACITOR A 3 F capacitor is given a potential difference across its plates of 10 V. What is the charge built up on its plates? If the source of the potential difference across the plates is removed, but the plates maintain their charge, what is the new potential difference across the capacitor if the distance between the plates is doubled? Page 4

5 CONCEPT: ENERGY STORED BY CAPACITOR Remember: Capacitors separate charges, and this separation leads to potential energy stored. But HOW MUCH energy? Energy stored by capacitor U - Remember that Q = CV ENERGY DENSITY ( ) = Energy per unit volume - Volume of a parallel plate capacitor = EXAMPLE: Two parallel plates of area 50 cm 2, with a separation of 10 mm, have a voltage across them of 20 V. What is the energy stored? The energy density? EXAMPLE: What electric field strength would store 2.5 mj of energy per cubic-centimeter? Page 5

6 PRACTICE: DEFIBRILLATOR A cardiac defibrillator can be modeled as a parallel plate capacitor. When it is charged to a voltage of 2 kv, it has a stored energy of 1 kj. What is the capacitance of the defibrillator? PRACTICE: ENERGY RELEASED BY FLASHBULB Typically, a flashbulb will have a capacitance of 1000 mf. If the bulb were charged to a voltage of 500 V, how much energy is released when the flash goes off, if the bulb loses 80% of its charge in a single flash? Page 6

7 EXAMPLE: SPHERICAL CAPACITOR (USING CALCULUS) What is the capacitance of two concentric spherical shells, one of radius a and one of radius b, with a < b? Consider the charge on each sphere to be +/- Q. +Q -Q a b EXAMPLE: CYLINDRICAL CAPACITOR (USING CALCULUS) What is the capacitance per unit length of two concentric, infinitely long cylindrical shells, one of radius a, and one of radius b, with a < b. Consider the charge on each cylinder to be +/- Q. Page 7

8 CONCEPT: COMBINING CAPACITORS IN SERIES AND PARALLEL In Circuit problems, you will need to COLLAPSE / COMBINE capacitors into a SINGLE capacitor. SERIES CONNECTION PARALLEL CONNECTION - Direct connection - Equivalent Capacitance: - Forms a loop - Equivalent Capacitance: EXAMPLE: What is the equivalent capacitance of the following capacitors? 2 F 1 F 2 F 4 F EXAMPLE: What is the equivalent capacitance of the following capacitors? 1 F 3 F 4 F 2 F Page 8

9 EXAMPLE: EQUIVALENT CAPACITANCE OF 4 CAPACITORS What is the equivalent capacitance of the following combination of capacitors? 2 F 2 F 5 F 3 F PRACTICE: EQUIVALENT CAPACITANCE OF 4 CAPACITORS What is the equivalent capacitance of the following capacitors? 2 F 3 F 2 F 2 F Page 9

10 CONCEPT: SOLVING CAPACITOR CIRCUITS In Circuit problems, you will need to find the CHARGE and VOLTAGE of different Capacitors. SERIES CONNECTION PARALLEL CONNECTION - Equivalent Capacitance: - Equivalent Capacitance: - Share [ CHARGE / VOLTAGE ] with EACH OTHER - Share [ CHARGE / VOLTAGE ] with EQUIVALENT Capacitor - Share [ CHARGE / VOLTAGE ] with EACH OTHER - Share [ CHARGE / VOLTAGE ] with EQUIVALENT Capacitor STEPS for Solving Capacitor Circuits: 1) Collapse down to ONE EQUIVALENT capacitor 2) Find VOLTAGE and CHARGE on Equivalent capacitor 3) Work backwards noting VOLTAGE and CHARGE on EACH capacitor EXAMPLE: What is the charge and voltage of each of the capacitors in the following circuit? 2 F 6 F 1 F 10 V Page 10

11 PRACTICE: FIND CHARGE & VOLTAGE IN ALL CAPACITORS What is charge and voltage across each capacitor below? 2 F 2 F 3 F 10 V EXAMPLE: FIND CHARGE OF ONE CAPACITOR What is the charge on the 3 F capacitor below? 1 F 5 V 3 F 2 F 4 F Page 11

12 PRACTICE: FIND VOLTAGE OF THE BATTERY What is the voltage of the battery below? 1 F 3 F 1 F V =? 3 C 2 F PRACTICE: FIND CHARGE OF CAPACITOR IN A COMPLEX ARRANGEMENT What is the charge on the 5 F capacitor? (hint: be careful with series vs parallel) Page 12

13 CONCEPT: INTRO TO DIELECTRICS Dielectrics [ INCREASE / REDUCE ] electric field strength within capacitors - The ability to reduce field strength = DIELECTRIC CONSTANT, > 1 ( = 1 for vacuum) - Dielectrics increase capacitance How Q, V, U and u change depends on how dielectric is INSERTED into capacitor: CONSTANT CHARGE (Q) CONSTANT VOLTAVE (V) - Q doesn t change - V - U - u - Q - V doesn t change - U - u EXAMPLE: A capacitor is connected to a battery as shown below. What is the charge on the capacitor after a dielectric ( ) is inserted into the capacitor while it is still connected to the battery? 9 V 3 F Page 13

14 EXAMPLE: CAPACITOR WITH A DIELECTRIC A capacitor has a voltage of 100 V when it has a charge of 2 C. A dielectric, with the plates are held at 100 V. What is the new charge of the capacitor?, is inserted into the capacitor while PRACTICE: CIRCULAR PLATE CAPACITOR WITH DIELECTRIC A parallel plate capacitor is formed by bringing two circular plates, of radius 0.5 cm, to a distance of 2 mm apart. The capacitor is made so that it has a dielectric of constant between the plates. When the charge on the capacitor is 3 nc, the voltage of the capacitor is 5000 V. What is the dielectric constant? EXAMPLE: CAPACITORS PARTIALLY FILLED WITH DIELECTRIC What is the new capacitance of the two capacitors that are partially filled with dielectrics shown in the following figure? A A L/2 L/2 d/2 κ d κ d/2 (a) (b) Page 14

15 CONCEPT: HOW DIELECTRICS WORK A DIELECTRIC is an insulating material that can - At the atomic level: Alone In external E Dielectrics [ INCREASE / REDUCE ] electric field strength within capacitors -Q + - +Q Page 15

16 CONCEPT: DIELECTRIC BREAKDOWN Dielectric is an insulator charges can t move IDEALLY - In REALITY, charges can move if voltage across insulator is large enough - This is known as DIELECTRIC BREAKDOWN DIELECTRIC STRENGTH = Electrons jump from atom to atom: +Q -Q e e Lightning is a common example of dielectric breakdown EXAMPLE: A parallel plate capacitor is filled with air and connected to a power source of 100 V. What is the closest you can put the plates together if dielectric breakdown of air occurs at an electric field of V/m? Page 16