Experiment 1:
RC Circuits
1
Experiment 1:
RC Circuits
Introduction
In this laboratory you will examine a simple circuit consisting of only one capacitor and one
resistor.
By applying a constant
1
voltage (also called DC or direct current) to the circuit, you will
determine the capacitor discharge decay time (defined later) and compare this value to that which is
expected.
Alternately, by applying alternating current (AC) and varying the frequency of the current
you will be able to determine the decay time in another, independent way.
You will determine these expected values using formulas derived from Ohm’s law, Kirchhoff’s
Law and the concept of complex impedance.
These concepts will be detailed further in the laboratory.
In addition to these new ideas you will need to recall the concepts from last week’s lab.
Specifically you will use the multimeter and oscilloscope during this lab.
Recall that the oscilloscope
must calibrated at the beginning of any experiment in which it is used.
1
Physics
1.1
Electrical Circuit Definitions
Any section of a circuit that is at constant voltage is called a “node.”
An example is a piece of wire
joining two or more resistors.
The sum of all the currents flowing into a node must be zero since charge
can neither be created nor destroyed in a circuit.
Circuit “elements” are resistors, capacitors, and inductors.
One might consider wires connecting
these elements to be a fourth circuit element but since idealized wires have no resistance, capacitance or
inductance they are represented only by lines in a circuit diagram and do not appear in the equations
relating current and voltage in circuits.
Figure 1
Resistors in series
Figure 2
Resistors R
4
and R
5
in parallel
1
Applying a square wave to the circuit is not exactly applying constant voltage.
However, if the period
of the square wave is long enough, you will not have to worry about what happens at the end when the
voltage switches from one constant voltage to another.
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Experiment 1:
RC Circuits
2
Two circuit elements are in series if all of the current flowing through one also flows through the
other.
In Figure 1, all of the current flowing from the battery must also flow through the resistors
R
1
and
R
2
.
They are “in series.”
In Figure 2, the current flowing through
R
4
does not flow through
R
5
(and vice
versa) so that
R
4
and
R
5
are not in series.
Two circuit elements are in parallel if they are connected to the same nodes.
R
4
and
R
5
in Figure 2
are both connected to nodes A and B.
This then also requires that the potential difference (voltage drop)
across all elements connected in parallel must be the same.
In more complicated circuits you will need to generalize the notions of series and parallel.
For
example,
in
Figure
2,
the
equivalent
resistance
of
R
4
and
R
5
in
parallel,
1
R
4
+
1
R
5
(
)
!
1
=
R
4
*
R
5
R
4
+
R
5
(
)
, is in series with
R
3
.
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 Spring '08
 Bodde
 Current, RC Circuits, Alternating Current, RC circuit, Electrical impedance

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