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E04-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Experiment 4: RC Circuits OBJECTIVES 1. To explore the time dependent behavior of RC Circuits 2. To understand how to measure the time constant of such circuits PRE-LAB READING INTRODUCTION In this lab we will continue our investigation of DC circuits, now including, along with our “battery” and resistors, capacitors (RC circuits). We will measure the relationship between current and voltage in a capacitor, and study the time dependent behavior of RC circuits. The Details: Capacitors Capacitors store charge, and develop a voltage drop V across them proportional to the amount of charge Q that they have stored: V = Q/C . The constant of proportionality C is the capacitance (in Farads = Coulombs/Volt), and determines how easily the capacitor can store charge. Typical circuit capacitors range from picofarads (1 pF = 10 -12 F) to millifarads (1 mF = 10 -3 F). In this lab we will use microfarad capacitors (1 μ F = 10 -6 F). RC Circuits Consider the circuit shown in Figure 1. The capacitor (initially uncharged) is connected to a voltage source of constant emf E . At t = 0, the switch S is closed. Figure 1 (a) RC circuit (b) Circuit diagram for t > 0 In class we derived expressions for the time-dependent charge on, voltage across, and current through the capacitor, but even without solving differential equations a little (a) (b)
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E08-2 thought should allow us to get a good idea of what happens. Initially the capacitor is uncharged and hence has no voltage drop across it (it acts like a wire or “short circuit”). This means that the full voltage rise of the battery is dropped across the resistor, and hence current must be flowing in the circuit ( V R = IR ). As time goes on, this current will “charge up” the capacitor – the charge on it and the voltage drop across it will increase, and hence the voltage drop across the resistor and the current in the circuit will decrease. This idea is captured in the graphs of Fig. 2. V f = ε Q f =C ε Q Capacitor , V Time V R,0 = ε I 0 = ε /R V Resistor , I Time Figure 2 (a) Voltage across and charge on the capacitor increase as a function of time while (b) the voltage across the resistor and hence current in the circuit decrease.
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This note was uploaded on 02/27/2011 for the course PHYSICS 8 taught by Professor Dourmashkin during the Fall '10 term at MIT.

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