Physics 2020
2.1
Experiment 2. Introduction to Circuits
In this lab, you will gain some experience using two basic electronic instruments:
a DC power supply, which produces an adjustable DC voltage, and a digital multimeter,
which can measure resistance and voltage. You will construct some simple circuits using
resistors and light bulbs and make measurements to check the validity of Kirchhoff's
Rules.
Let us review some of the fundamentals of electric circuits. The resistance R of a
circuit element is defined as the ratio of the voltage drop across the element to the current
flowing through it,
R=
(1)
V
.
I
If the resistor is ohmic, then the ratio V/I is a constant, independent of current or voltage,
and the resistance is constant. However, many materials, such as light bulb filaments, are
non-ohmic; their resistance depends on the applied current and voltage. When a light
bulb filament is glowing white hot, its resistance is much greater than when it is cool.
Resistors can be combined in series or in parallel. The total resistance of several
resistors in series is just the sum of the individual resistances. Note that the total series
resistance is always larger than any of the individual resistances.
(2)
R total = R 1 + R 2 + R 3
R1
R
3
R2
(series)
The total resistance of several resistors in parallel is always smaller than any of the
individual resistances according to the formula:
R1
1
1
1
1
=
+
+
(3)
(parallel)
R tot R 1 R 2 R 3
R2
In the case of two resistors in parallel,
equation (3) becomes:
(4)
R tot =
R 1R 2
R1 + R 2
(parallel).
Kirchhoff's junction rule states that, in steady
state, the sum of the currents flowing into a junction
must be equal to the total current flowing out of the
junction (otherwise charge would be building up at the
junction, and we would not be in steady state.) In the
© University of Colorado at Boulder, Dept. of Physics
R3
R1
I1
R2
I2
R3
I3
Physics 2020
2.2
example shown here, there are two currents I1 and I2 shown flowing into a junction and
one current I3 is coming out. The junction rule says that I1 + I 2 = I 3 .
Kirchhoff's loop rule states that, in traversing any closed loop in a circuit, the
sum of the voltage rises must equal the sum of the voltage drops. You can think of
voltage as a kind of electrical pressure. Voltage differences push charges through an
electrical conductor, just as pressure differences push water through a pipe. Water in a
pipe always flows from regions of high pressure to regions of low pressure, except in a
pump, which forces the water to flow toward high pressure. Likewise in a circuit,
(positive) charges flow from high voltage to low voltage, except within a battery or
power supply, which forces the charges "upstream" toward higher voltage. The voltage
at a point in an electrical circuit, like the pressure at a point in a network of pipes, has a
constant, well-defined value. If we traverse any closed loop in a circuit, or in a network
of pipes, we must return to our original voltage (or pressure). Thus the total
voltage(pressure) drop must just equal the total voltage (pressure) rise.
The two instruments you will use in this lab
are a DC power supply and a digital multimeter.
The DC power supply produces a constant voltage,
voltage
coarse which can be adjusted from between zero and 30
volts with the voltage knob on the front panel. The
voltage
power supply has three output terminals: plus
fine
(red), minus (black), and ground (green). The
ground terminal is always at zero volts. In this
experiment, the ground and minus terminals are
current
tied together by a metal connector so the minus
current
terminal is also at zero volts. Both the current and
voltage produced by the power supply can be read
+
on meters on the front panel. Also on the front
panel is a current-limit knob, which can be
adjusted to limit the maximum output current, to
metal connector
prevent damage to sensitive circuit elements. In
this lab, the current knob has been set and clamped in place so the power supply cannot
produce more than about 0.6A current.
DC Power Supply
-
The hand-held digital multimeter (DMM) is a wonderful little device which can
be used to measure voltage and current (DC or AC), resistance, and capacitance. In this
lab, we will use it to measure resistance and DC voltage only. When making any
measurement, there are always 2 wires to the DMM. One of the two wires always goes
to the COM (common) terminal. To measure voltage or resistance, the second wire is
attached to the V_ input. In this lab, all our measurements will be DC, so the DC/AC
switch (upper right) should always be in the DC position. The DMM has an alarm; it
sings if you have wires plugged into positions which conflict with the central knob’s
position. (For instance, if you have the wires in COM and VΩ, but have the center knob
in the "Amps" quadrant.)
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Physics 2020
2.3
The DMM has two special cables called "needle probes" - long wires with pointed
metal ends. You can quickly measure the voltage between any two points in a circuit by
touching the points with the needle probes.
When measuring a
resistance with a DMM,
you must disconnect the
source of the resistance
(be it single resistor or
some combination of
resistors) from any other
devices, such as power
supplies. Never try to
measure the resistance of
a resistor while it is in a
circuit.
V
Measuring a resistance
with the DMM.
DC
DC AC
V
DMM
Ω
com VΩ
needle probes
Procedure
resistor
Part I. Measurement of resistance
Each position should have 5 resistors: one 15Ω, one 40Ω, one
1500Ω, and two 3000Ω resistors. These values for the resistances are
given by the manufacturer and are approximate. Each resistor is mounted
in a double-banana plug connector. Begin by carefully measuring the
resistance of each resistor with your DMM and record your measured
resistances. The double-banana mount can be plugged directly into the
DMM, without using any wires.
There are also two light bulbs at each position. Use the DMM
with the needle probes to measure the resistance of each light bulb
filament. Remember to always record your measurements directly in
your lab book in ink.
Take the three large-valued resistors (the 1500Ω and the two
3000Ω resistors) and place all three in parallel, by stacking the doublebanana plugs as shown in the diagram. Now use the DMM to measure
the total resistance of this parallel combination of three resistors.
Compare your measured Rtotal with the value you expect from your
earlier measurement of the individual resistances and equation(3).
© University of Colorado at Boulder, Dept. of Physics
Physics 2020
2.4
Repeat this procedure for some other combination of resistors in parallel and
some other combination of resistors in series.
Use the DMM with needle probes to measure the resistance of your body between
your right and left hands. Measure the resistance by holding the probes tightly with dry
hands. Then wet your fingers and repeat the measurement. You will find that wet skin
has a much lower resistance than dry skin. (Stabbing each hand with a probe would
result in an even smaller resistance, but this procedure is not recommended.)
Part 2. The resistance of a hot light bulb filament.
Using connecting wires and the "plug board", build a circuit consisting of the DC
power supply in series with the15Ω resistor and one light bulb. Whenever you build any
circuit with a variable voltage source, you should always make certain that the voltage is
turned down to zero (fully CCW) before connecting any wires.
Circuit Schematic
DC voltage souce
V= 0 - 30 V
15 Ω
light bulb
Physical Layout
light bulb
power supply
plug board
resistor
Slowly, turn up the voltage until the bulb begins to glow brightly (not too bright,
we want the bulbs to last!). Now using the DMM with needle probes, measure the
voltage V across the power supply terminals, the voltage VR across the 15Ω resistor and
the voltage VB across the light bulb. Using the known resistance of the resistor
(measured in Part I), compute the current IR, though the resistor. The current though the
light bulb IB is equal to IR, since the resistor and bulb are in series. From these
© University of Colorado at Boulder, Dept. of Physics
Physics 2020
2.5
measurements, you can compute RB, the resistance of the bulb. Compare with the value
you measured in Part I. Why are they different?
Part 3. Qualitative investigation of circuit behavior.
Construct the circuit shown below, consisting of two light bulbs in series with the
power supply. (The resistor R will be added later). Slowly increase the voltage until the
bulbs are glowing (not too bright!). Now place the R = 40Ω resistor in parallel with bulb
2 as shown. What happens to the brightness of
the two bulbs? Explain.
R
Repeat this procedure with R = 1500Ω
and R = 15Ω. What happens in each case?
Explain.
2
1
V
Part 4. Kirchhoff's Laws.
Construct the following circuit (Remember to keep the voltage turned down to
zero, initially!). Increase the power supply voltage to about 10V. Now measure the
voltage across the power supply terminals and across each resistor. From your measured
voltages and the resistances you measured in Part 1, compute the current through each
resistor. Use your measured voltages and computed currents to verify Kirchhoff's loop
rule and current rule.
R
3000Ω
1500Ω
V
3000Ω
© University of Colorado at Boulder, Dept. of Physics
Physics 2020
2.6
Prelab questions. (Due at the beginning of your lab session, as usual.)
1. Show the "missing algebra" to drive equation (4) from equation (3) in the case
of two resistors in parallel.
2. Suppose the resistance of your body between your right and left hands is
Rbody=500kΩ. What would be the current through your body if you touched
the plus and minus terminals of the power supply used in this lab, with the
voltage knob on the supply is turned all the way up? The threshold of
sensation for electric current through your body is about 300µA. Would you
feel the current?
3. Suppose all 5 resistors used in this lab were placed in parallel. What would be
the total equivalent parallel resistance? What would be the total resistance if
all 5 resistors were placed in series.
4. What do you predict will happen to the brightness of each bulb in part 3 of
this lab when you place a resistor R in parallel to bulb #2. Answer
qualitatively: bulb so-and-so becomes "brighter", "dimmer", or "stays the
same". Justify your answer with words or equations.
5. Make a sketch to show how you would connect two light bulbs in parallel to
the power supply .
6. Dry Lab
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