ECEN 1400
HW 1
Resistors
ECEN 1400, Introduction to Analog and Digital Electronics HW 1: Resistors (100 pts) 1. SERIES RESISTANCES (10 PTS)
Consider two resistances in series connected to an ideal voltage source, as shown. Apply
Ohm’s Law to each resistor independently (Hint: you need symbols V1 and
V2 but only a single current I).
a) Noting that the current through both resistors is the same, prove that you could
replace these two resistors with a single equivalent resistance whose value is the
sum of the two resistors.
b) Write Ohm’s Law for this equivalent resistance. Using the three equations (all
Ohm’s Law), derive the voltage divider equations. That is, what are the voltage
drops across R1 and across R2 in terms of just V, R1 and R2?
2. PARALLEL RESISTANCES (10 PTS)
Consider the two resistances in parallel across an ideal source, as shown. Write Ohm’s
Law for each resistor but use the conductance of each resistor G = 1/R in the equation.
a) Noting that the voltage across both resistors is the same, prove that you could
replace these two conductances with a single equivalent conductance whose value
is the sum of the two conductances. Substitute in G = 1/R and write the equation
in terms of resistances, which is generally the more useful form.
b) Write Ohm’s Law for this equivalent conductance. Using the three equations (all
Ohm’s Law), derive the current divider equations. That is, what is the current
through G1 and G2 in terms of just the current from the source (I), G1 and G2?
Again, write these in terms of R1 and R2 once you have derived it.
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R. McLeod
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ECEN 1400
HW 1
Resistors
3. PRACTICE PROBLEMS WITH OHM’S LAW (20 PTS)
Use Ohm’s law, the divider equations and/or equivalent resistors to solve the following:
a) (5 pts)
b) (5 pts)
c) (5 pts)
d) (5 pts)
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R. McLeod
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ECEN 1400
HW 1
Resistors
4. DESIGN PROBLEM WITH OHM’S LAW (20 PTS)
It is quite common that you have a fixed supply voltage and need to generate some other
analog voltage. The voltage divider is the solution to this problem. Usually, we don’t
want a lot of current to flow, which would cause power dissipation and thus heat. Design
a circuit to meet the following conditions:
• The voltage across R2 (measured by the volt meter) is 10 volts.
• The input voltage VIN is 50 volts.
• The minimum amount of current (I) flows.
• You have resistors available between zero and 1 MΩ (one million Ohms).
Show your work neatly and make the solution easy to find. How much power is
dissipated in your circuit?
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R. McLeod
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ECEN 1400
HW 1
Resistors
5. PRACTICE WITH RESISTOR COLOR CODES (10 PTS)
Write the value and tolerance of each resistor. 1
1
http://www.rmroberts.com/FTP_files/ResistorColorCodeHandout.pdf
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R. McLeod
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ECEN 1400
HW 1
Resistors
6. USING NI MULTISIM FOR SCHEMATIC CAPTURE AND SIMULATION (30 PTS)
•
This problem uses Multisim, which you installed as part of HW 0 (right?). Since
this is the first time, I will walk you through each step.
•
Open the multisim application in the Circuit Design Suite folder. You will see a
bunch of toolbars and a blank schematic:
•
Right click on the blank schematic and select the top entry which is Place
Component. This brings up the library of electrical components. There are lots
and they are very complete models.
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R. McLeod
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ECEN 1400
HW 1
Resistors
•
Select the Sources group from the left drop-down menu and the
POWER_SOURCES family. Left click on GROUND which will close the
window and allow you to place a ground symbol on the schematic by clicking on
the desired location. You will be returned to the component selection window.
Select DC_POWER and place it on the schematic. Finally, select the group
Basic and the family RESISTOR and select a 470 ohm resistor. Press “control
R” to rotate the resistor so it is vertical and place it on the schematic. Close the
select component window. You should now have a schematic with three
components on it:
•
We could now insert simple meters from the Indicators group of the components,
but let’s instead do something a bit more fun that will directly prepare you for the
lab. Left click on the Simulate menu on the top bar, select Instruments and then
Agilent Multimeter. This is a complete functional simulation of the bench top
multimeter you will use in the lab. Repeat the procedure to insert a second
multimeter (in the lab we’ll use a handheld multimeter here).
Now left click on the wire ends of any component and wire up the circuit as
shown. I have put in text labels for voltmeter and ammeter to make the diagram
clear, but you don’t have to. You may need to insert a junction (a place where
two wires are connected) via right click, then Place on Schematic then Junction.
Note the specific connections to the multimeter terminals. These are the same
ones you will use in the lab. You should now have:
•
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R. McLeod
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ECEN 1400
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HW 1
Resistors
Now double click on each meter to open their front panels. Note which meter is
which via the XMMx labels. Turn the meters on (yes, with the power button) and
put them into the proper modes following the instructions in the lab 1 write up.
Isn’t this the coolest thing you have seen today? Select Run under the Simulate
menu. Your meters should now show
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R. McLeod
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ECEN 1400
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HW 1
Resistors
Double-click on the power supply to bring up a menu to change its voltage, ditto
for the resistor to change its resistance. Using this tool, do part 4 of lab 1 for a
single resistor value. Graph the results, just like you will for the lab (use a
graphing program like matlab or excel and keep the file so you can rapidly use
this for your post-lab). Confirm that your results match Ohm’s Law. Turn in a
printout or screen capture of your schematic.
EXTRA CREDIT (2 PTS PER PROBLEM 3 (A-D) AND 4, 10 PTS MAX)
Check your work by putting the circuit into multisim. Turn in a screen capture showing
the correct currents or voltages using the simple meter indicators.
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R. McLeod
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