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6 Capacitors 2008

# 6 Capacitors 2008 - C.1 CAPACITORS THE FUNCTION O F CA PA C...

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C.1 hermannWellenstein Spring 08 CAPACITORS T HE F UNCTION OF C APACITORS IN E LECTRIC C IRCUITS , P ULSER . A. I NTRODUCTION : The purpose of this experiment is to learn about the function of capacitors in electric circuits. The capacitor, next to the resistor, is the most important electric circuit element. It has the capacity of storing electric charge, and its function is sometimes compared to containers filled with liquid or gases. Although charging and discharging of containers through tubes follow similar mathematical laws, there is a limit of this analogy. Electric circuits are governed by the interaction of freely moving electrons with "stationary" positive ions (and neutrals). This requires that electric circuits are "closed loop", whereas a reservoir discharging through a tube is "open loop".

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CAPACITORS C.2 Hermannn Wellenstein Spring 08 B. T HEORY : The simplest capacitor consists of a pair of parallel plates. If connected to a battery, electrons flow away from one plate, making it positive, to the other, which becomes negative. The resulting electric field gradually brings the flow to a stop. Here, we only collect the formulae we need for the experiment; refer to the lecture notes and the book for more detail. The equations below describe the behavior of a capacitor qualitatively. The charge on a capacitor is Q = C V, (1) where Q is the charge in Coulombs, C is the capacitance in Farads, and V is the Voltage in Volts. Discharging of capacitor : (See Figure 1.) If Q = Q o at t = 0, then Q = Q o e ! t / RC (2) but Q = C V and Q o = CV o , hence, V = V o e ! t RC = V o e ! t " (3) Charging of capacitor : (See Figure 2.) If V = 0 at t = 0, then V = V o 1 ! e ! t RC " # \$ % & (4) where V o = V , at t = ! . τ = RC is the characteristic time of the RC-circuit. In time τ the voltage (or the charge) decreases by the factor e = 2.72, i.e. to approximately one Figure 1. R C V t V 0 0 V 0 Figure 2.
CAPACITORS C.3 Hermannn Wellenstein Spring 08 third. Before coming to lab, show, by using the definitions of R and C, that the units of τ are sec.

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