DC Circuits
1
Physics 364
Objective
In this lab we will get a basic introduction to the most fundamental concepts of electronics:
voltage, current, and resistance. We will also use this lab to familiarize ourselves with the
breadboards upon which we will build circuits all semester and with the oscilloscope–the
single most important test instrument for circuits. We will also begin to learn about circuit
design by testing Kirchhoff’s Laws and by exploring the voltage divider, the simplest, but one
of most important, circuits in all of electronics. We will learn about loading and Thévenin
Models. None of this lab is very hard; it is basic. But we have to understand these ideas very
well to move on to the good stuff that includes active devices like transistors and gates. “A
journey of a thousand miles...”
2
The Breadboard
Use an ohm meter to determine which sets of holes on the breadboard are electrically connected together. Draw a diagram in your notebook showing which sets of holes on the breadboard are connected (for example, by drawing a solid line through connected holes).
3
Ohm’s Law
Build the circuit shown in Fig. 1 on your breadboard. Verify that the resistor obeys Ohm’s law.
You must determine an appropriate procedure to do this. Record your procedure in your lab
notebook. Record your data in a neat table and graph the results. Be sure to estimate the
uncertainty in your measurements. Explain how you analyze your data to determine R. Test
two resistors: one with a resistance of about 20 kΩ, and a second with a resistance of about
10 kΩ. You may not be able to find resistors labeled with exactly these values. Remember that
voltages are measured across circuit elements (i.e. between points in a circuit) and currents
are measured through circuit elements.
Figure 1: Your first circuit
Some important points on building circuits throughout the semester:
Physics 364
DC Circuits
1. Don’t build your circuit in the air, use the breadboard and begin to learn how the breadboard functions. We will be using it all semester. Bring the power supply and meters
to the breadboard through banana jacks and plug wires into the breadboard to connect
circuit devices (in this case a resistor) to the appropriate jacks. Figure 2 shows a good
way and a bad way to build a circuit.
Figure 2: Examples of bad and good breadboarding, respectively.
2. Use color coding of wires e.g. black for ground and red for the positive supply (other
colors are fine, but you should be consistent in a particular circuit).
3. Place the positive supply on a bus strip above the circuit and ground on a strip below
the circuit. If you use a negative supply (in future labs) place it on a strip below ground.
4. Build your circuits neatly and logically on the breadboard so that it is easy to troubleshoot them. Diagnosing a circuit can be difficult; don’t make it worse by having a
poor layout on the breadboard.
In order to verify Ohm’s Law for the resistor, you need to measure the voltage across the
resistor and the current through the resistor. However, in the circuit of Fig. 1, one of the
instruments is not making the correct measurement. Which instrument is it and why isn’t it
making the right measurement? Draw a new circuit showing the location of this instrument
so that it does make the right measurement. Does the other instrument now make the right
measurement? What does this tell you about the desired internal resistance of ammeters and
voltmeters?
4
Kirchhoff’s Laws
Design and construct two circuits using the DC power supply and three or more resistors (1 kΩ
to 10 kΩ) to demonstrate the Kirchoff Voltage Law (i.e., the Loop Rule) and the Kirchoff Current Law (i.e., the Point Rule). Check your circuit with me before you construct it. Calculate
the DC voltages in the circuit using the two laws and then compare them to measurements
that you make with the DMM. For each circuit, pick one node and verify that your measured
values of current satisfy the KCL. Pick one loop and verify that your measured values of voltage
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Physics 364
DC Circuits
satisfy the KVL. Draw a “voltage map” for the loop, i.e., draw a graph of voltage vs. position
in the loop. Label points on your circuit and on your graph so I can compare them accurately.
Answer the following questions:
1. Express the KCL (Point Rule) in words. What conservation law is involved?
2. Express the KVL (Loop Rule) in words. What conservation law is involved?
5
The Voltage Divider
Build an unloaded voltage divider (see Fig. 3, for an example circuit) using a power supply and two 10 kΩ resistors. Draw the circuit in your lab book. Apply Vin = 10 V.
R1
Vin
+
Measure the open-circuit voltage Voc with a DMM. Attach
Vout
a 10 kΩ load to the output terminals of the voltage divider
and measure the output voltage. How does it compare to
R2
Voc ? Measure the output voltage for three other values of
R L and graph the results.
Now measure the short circuit current Isc . Do this by
connecting the output terminals together through the ammeter. In this case you don’t need to be worried about
Figure 3: A voltage divider
shorting the output terminals. Explain why in general it
can be dangerous to short a circuit, and why it’s not dangerous in this case.
Calculate the Thevenin equivalent voltage Vth and resistance R th based on your measurements of Voc and Isc . Also calculate Vth and R th from the values of your circuit elements using
the theoretical expressions for Vth and R th. Do these calculations agree?
Build the Thevenin equivalent circuit using your calculated values of Vth and R th. Verify
that this circuit has the same values of Voc and Isc as the original voltage divider. Measure
the output voltage for the same values of load resistance as you used above. How does the
output voltage of the Thevenin equivalent circuit compare to the output voltage of the voltage
divider?
Suppose you wanted your voltage divider to supply 5 V to a 10 kΩ load. Do you have
a problem? How might you change the circuit to avoid this problem (without changing the
power supply)? Hint: do you want R th to be large, small, or about the same compare to R L ?
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Physics 364
DC Circuits
Propagation of Error
The rules for propagating an uncertainty depend on whether the quantity that is being computed is the result of a sum, different, product, or quotient operations. The following rules
guide your calculations.
If q = x + · · · + z − (u + · · · + w), then the uncertainty in q is given by
p
δq = (δx)2 + · · · + (δ y)2 + (δu)2 + · · · + (δw)2 .
If q =
x×···×z
,
(u×···×w)
then
δq
|q|
È
=
δx
x
2
+ ··· +
δz
z
2
+
Page 4
δu
u
2
+ ··· +
δw
w
2
.