Lab 1 Use of the DMM and Oscilloscope
Use of the Digital Multimeter
The digital multimeter(DMM) allows for a variety of circuit properties to be
measured. The meters at your benches have 10 Megohm input impedance.
This allows one to measure voltages across elements whose impedance is much
smaller than 10M Ω.
(1) Obtain two each of the resistors listed in Table 1.1. The exact values are
not important. Use the DMM to measure the resistance of each resistor. Remember which resistor is R1 and which is R2 when filling out the table.
Table 1.1
Rnominal
R1 (Ω)
R2 (Ω)
390
75K
1.2M
10M
Set Vps and record its value,
Vps =
Vab(V)
(2) A voltage divider is a string of resistors as in fig.1.1 It is easy to show that
Vab =
R2
R1 +R2 Vps
(eq.1)
Set up the circuit in fig.1.1 with the variable power supply Vps set at about
10V. Measure Vab and record the values in Table 1.1.
Question: Is eq.1 satisfied for for each of the four combinations in Table 1.1?
Where is the disagreement the worst? What is the reason for the disagreement?
(3) Complex combinations of batteries and resistors can be replaced by equivalent circuits according to Thevenin’s theorem. We will check Thevenin’s theorem for the case in fig. 1.2.
(a) Obtain 4 390Ω resistors and set Vps to about 2V. Measure all these quanties
with the DMM and record them. Our goal is to predict the current in the load
resistor RL .
(b) We wish to find the circuit ( fig. 1.3) which is equivalent to fig. 1.2. To
obtain Veq we simply leave a-b open. Measure Vab = Veq=
.
Now there are two ways to obtain Req . Set the DMM to read current (A) and
short circuit a-b with the DMM in the current reading mode as in fig. 1.4.
current I’ =
, therefore Req = Veq /I’ =
.
In the second technique we remove Vps entirely and replace Vps by a short circuit as in fig. 1.5. Now measure the circuit resistance with the DMM set on
the resistance mode
Req =
Do the two values you obtained for Req from figs. 1.4 and 1.5 agree? What
could be the reason for the difference?
Choose a resistor RL between 100 and 500Ω. Measure the resistance with the
DMM. The predicted current IL is
IL =
Veq
Req +RL
L
or equally well we expect Vab = Veq RLR+R
eq
when RL is placed across a-b. Measure Vab and compare it to what you expected from the voltage divider equantion.
Use of the Oscilloscope
The oscilloscope is one of the most useful laboratory instruments. It enables
observation of the shapes, magnitudes and relative time differences between two
pulses.
(a) Pulse shape and time measurements
Connect the sine wave oscillator as shown in fig. 1.6 to the input of the oscilloscope.
Adjust the amplitude of the sine signal to get a convenient amplitude on the
screen. The sine wave generator will have a dial reading frequency. Choose
four widely separated frequencies and measure the periods using the oscilloscope. Compare the true measured periods to those deduced from the sine
wave generator dial readings. The large discrepancy you will probably find is a
warning. Don’t trust the nominal dial readings in instruments!
(b) Phase relationships in a RC circuit
Construct the circuit shown in fig. 1.7. We will measure the current i through
the 1000Ω resistor and the voltage v(t) as a function of frequency. The phase
angle, φ, between i and v is given by (ω = 2πf )
1
)=
φ = arctan( ωRC
2π∆t
T .
In this exercise we will leave RC fixed and vary the frequency f. Notice that we
measure i by measuring the voltage v across the 1000Ω resistor.
Table 1.2
Fill out a table such as the one below. The frequencies are nominal. You will
determine the true period by measuring it on the oscilloscope.
fnominal (cps) T(seconds) ∆t(seconds) φ = 2π∆t/T φ theory
50
100
1000
2000
10000
100000
Notice that φ is calculated in radians.