The Oscilloscope and AC Circuits (Lab 09)

If we applied this sinusoidal voltage source to a resistor, then Ohm’s law would tell us that the
current through the resistor at any instant of time would be given by
V V0
i sin( t)
I
0
sin( t)
.
R R
Note that every time the voltage V reaches a maximum, the current i reaches a maximum. The
same is true for the voltage and current reaching zero or a minimum. We then say that, for a
resistor, the voltage and current are "in phase." Note also that Ohm’s law relates the amplitudes
V 0 and I 0 .
This behavior is not the same for a capacitor or an inductor when connected to a sinusoidal
voltage source. This is because the voltage and current in these devices are related to each other
through a time derivative. For instance, the voltage across an inductor is proportional to the rate
of change of current (di/dt) and not simply to i. For inductors and capacitors, the voltage and
current are not in phase. You will learn, in fact, that for a single inductor or a single capacitor
connected to a sinusoidal source, the current and voltage are 90° out of phase. In other words,
when V reaches a maximum or minimum, i is zero and vice-versa. For a capacitor, the current i is
90° ahead of the voltage, and in an inductor, the current is 90° behind the voltage. The
amplitudes I 0 and V 0 are related to each other by something that sort of looks like Ohm's Law:
V
0
I
0
V0
I
0
X
C
C
I X I ( L)
0
L
0
for a capacitor
for an inductor
(Eq. 1)
Note that the quantity that looks like a "resistance" (technically called a "reactance") changes
with frequency! From Eq. 1, we can see that a capacitor acts like it has a high reactance at low
frequencies and a low reactance at high frequencies, while for an inductor it's the other way
around.
Today's lab will focus on a "series RLC" circuit in which we connect a resistor, a capacitor and
an inductor in series with a sinusoidal voltage. (We will use the oscilloscope to observe what
happens as we vary the frequency of the driving voltage). The circuit is as shown below:
R
V = V 0 sin(ωt)
C
Figure 1 A series RLC circuit, in which a sinusoidal voltage source V, drives a current through a resistor R, an
inductor L and a capacitor C.
L