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Transcript
Honors Physics Power-Point 6-5 CAPACITORS WHAT IS A CAPACITOR? Capacitors store electric charge and decay through exponential means. They are made out of two parallel plates with a material (typically waxed paper) between them. This material is called a dielectric. APPLICATIONS OF CAPACITANCE It all began with the Leyden jar (demonstrated earlier). It is now used in computers, radios, televisions, and camera flashes. THE DEFINITION OF CAPACITANCE It is the charge stored per unit voltage. It is measured in a unit called a Farad. (It is named after Michael Faraday (1791). Q Coulombs C Farad V Volt EXAMPLE #1: USE OF DEFINITIONS A 12.0 V battery is connected to a parallel plate capacitor which is rated at 1.0 micro-Farads. The plates are separated by 0.00600 m of dry air. (a) What is the charge on each plate? (b) What is the electric field exactly between the plates? FACTORS AFFECTING CAPACITANCE The relative permittivity (K) indicates the degree to which a capacitor can hold its charge. EXAMPLE 2: FACTORS AFFECTING CAPACITANCE A parallel plate capacitor consists of two metal plates separated by 0.00600 m of dry air. The capacitor is connected to a 100 V source. The area of each plate is 0.0400 m2. C o A C d o A d Where k= relative permittivity (k=1 here) The permittivity constant is 8.85 X 10-12 (a) What is the value of the capacitance? (b) What happens when the area of the plates is increased? (c) What happens when the distance between the plates is increased? EXAMPLE 3: RELATIONSHIP TO ENERGY To derive expressions for energy stored in a capacitor, we must appeal to integral calculus. (We only need to use the results here!) EXAMPLE 3: ENERGY IN A CAPACITOR A 1.0 pF capacitor is hooked up to a 9.0 V battery. (a) What is the charge stored? (b) What Is the energy stored? EXAMPLE 4: CAPACITOR DECAY Derive the exponential decay equation for Voltage in a capacitor. EXPRESSION FOR EXPONENTIAL DECAY V Voe kt The constant k is the time constant for a circuit and is equal to 1/RC (proven through differential equations—well beyond the scope of the course. EXAMPLE 4: CAPACITOR DECAY A 9 V battery is connected to a 100 kilo-ohm resistor and a 1 micro-Farad Capacitor. (a) What is the time constant for this circuit? (b) What is the time that half the value of the voltage decays?