PHY132 Labs (
©
P. Bennett, JCHS) -1-
08/11/04
PHY 132 LAB LRC circuit (phases)
Introduction
"Phase" means the relative advance or retardation (expressed in radians) of
one wave with respect to another. Two waves whose crests coincide are said to be
"in phase" - if the crests of one lie over the valleys of the other, they are pi out of
phase.
It is only simple to define phase for waves of the same frequency. In this
lab we will measure the phase difference between voltage and current for each
component in a series LRC resonant circuit. The purpose of the lab is teach you
about the concept of phase and reactance in AC electrical circuits. Resonant
circuits are used in oscillators to generate radio waves, and are studied with this
same circuit in the next lab.
In this experiment we compare the phase of the
voltage across "reactive" components (inductance, capacitance) with that of the
current, which is the reference. (The phase of the current is equal to that of the
voltage across any resistor , so we actually measure voltage instead. Voltage and
current are "in step" across a resistor, but not across a capacitor or inductor).
Capacitors and inductors have "Reactance", which is a kind of frequency-
dependant resistance, and is used for inductors and capacitors because these circuit
elements change the phase relationship between current and voltage through them,
unlike a resistor. We will see that Ohm's still holds in frequency-dependant form
for reactances.
Theory
R
C
V_in
L
Fig. 1 Generic series LRC circuit.
Consider the steady-state (sinewave) behavior of a series LRC circuit as
shown in Fig. 1. By definition, the same current flows through each component of
a series circuit (it has the same value everywhere in the circuit at any particular
time) and can be written as
i(t) = I
0
sin(
ω
t)
eq. 1

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