Lab 1: Ohm’s Law and Kirchhoff’s Law Name: ___________________________________
BIOE 3010: 2020
Objective: Simulate Ohm’s Law and resistor nets.
Skills learned: How to construct a circuit in LTSpice.
Deliverables: Answer the questions on this page and turn it in at the beginning of class on Friday 9/1. You may work with a partner for this lab, but everyone needs to turn in their own lab.
Score: This lab is worth 41 points, plus one bonus point.
Ohm’s law: the voltage across a resistor is the current through it multiplied by its resistance (V = IR). Note the language used – voltage across and current through (never never never refer to the voltage through something or the current across it)
Figure 1
Usually the triangle on the left will be used to symbolize ground, but they all mean 0V
You will need to use LTSpice to complete this lab. If you haven’t downloaded it please do so now.
https://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html
LTSpice is a circuit simulation program that allows you to test your circuits before you build it. Today we will use it to confirm Ohm’s law and explore the effects of resistance on a circuit.
Resistors, as their name implies, resists the flow of current through the circuit. Without resistance, current would flow quickly through a circuit and is known as a ‘short’. This would drain a battery very quickly and overheat the circuit.
We will first start with a new schematic. There are a limited array of components you can select in the toolbar. The first thing we need to do is place our resistors (shortcut key is simply ‘r’) place two resistors in series. If you want to rotate the resistor, press ‘Control r’ before placing. Then we need a voltage source, either select this icon or use F2. Then wire them together as shown in figure 2.
For simulation we need to indicate ground, so attach ground to the negative side of the battery.
Next we need to select values for the circuit. V1=5V, R1=100 and R2=1k. The resistances are understood to be in Ohms, and 1k is understood to be 1kΩ=1000Ω. The default voltage is going to be direct current (DC), though for other labs we can create alternating current (AC) or generate specific frequencies.
Figure 2
Figure 2Next to start the simulation select or select ‘Simulate’-> ‘Run’. You will be presented with a ‘Edit Simulation Command’ window. Since this simulation doesn’t deal with frequency ranges, voltage sweeps or is time dependent select the ‘DC op pnt’ tab and select ‘OK’ to plate the text .op in the schematic. The text can be anywhere on the schematic.
Once you have done this you should get a window that gives you all the necessary information. Once you close this window you can move your cursor over the components to get even more information. For instance, the power dissipation across R2, in this simulation is 20.661156mW. To fill out the table below we only need the voltage across R2, and the current through R2. In apple close the plot window and select L.
Figure 3
Figure 3Measure and plot the voltage across a 1k resistor as you vary the current through it. Change the value of “R1” so that you get different values for current through R2 and fill out the table and plot the data in excel with a trend line and equation. Include the plot with this submission. (5 points)
R1 [Ω]
VR2 [V]
IR2 [mA]
100
4.54545 V
4.54545mA
330
10k
330k
500k
1M
(a)
<>
Figure 4
Figure 4Again, repeat with the resistor in parallel. Fill out the table and plot as before. (3points)
R1 [Ω]
VR2 [V]
IR2 [mA]
100
330
10k
330k
500k
1M
(b)
<>
Power is defined as the voltage across multiplied by the current through a component (P = IV). In resistors, power is dissipated as heat. Our resistors can dissipate 0.25W before something bad happens to the resistor. What would happen to the resistor if you dissipated more than 0.25W? ________________________________________________________________(2 Points)
How much resistance do you need to dissipate about 0.25W using a +5V supply? (2 points) __________________________________________________________________________
Place the resistance (calculated above) between +5V and ground and use LTSpice to measure the voltage across the resistor and the current through it to verify the actual power dissipated. (1 Point each)
Measure the voltage: _______________________________________________________
Measure the current: _______________________________________________________
What is the power? ________________________________________________________
What would happen to the resistor physically? ___________________________________
Resistors are often used to limit the amount of current through circuits (like in LEDs and pushbuttons). You can use Ohm’s Law to pick a resistor to prevent a circuit from using too much current or use a resistor as a sensor (measuring the voltage across a resistor is equivalent to measuring the current through it). By using two resistors, you can make any voltage.
Our first circuit block that is the voltage divider. Think of a “circuit block” as a circuit with an input and an output voltage
Circuit block
where Vout = f(Vin). By following certain rules, circuit blocks can be stacked to linearly combine the functions of each block. Complicated circuits are often just combinations of simple blocks. We will add a new block to our library of tools in each lab. Focus on how each block works, how to build and debug it, and you’ll have some very sophisticated circuits in no time!
Figure 5: LTSpice single voltage divider equivalent
Figure 5: LTSpice single voltage divider equivalentA voltage divider is composed of two resistors in series with an output between:
You have simulated this in question 1(a). The output is essentially the voltage across R2.
Kirchhoff’s Laws:
Current Law: The algebraic sum of currents in a network of conductors meeting at a point is zero, (current in = current out)
Voltage Law: The directed sum of the potential differences (voltages) around any closed loop is zero.
Derive Vout in terms of R1 and R2, (3 points)
Vout = ___________________________________________________________________
Design a voltage divider where Vin = 5V and Vout = ~1.16V. What ratio of resistors is required? (2 points) ___________________________
Now you must pick resistor values to make that ratio. Build three versions of the voltage divider: with resistances in the (a)hundreds, (b)thousands, and (c)tens of thousands of ohms. Label the schematics below and measure the actual Vout and I. (2 points each)
(a)
(b)
(c)
R1 =
R2 =
I =
Vout =
R1 =
R2 =
I =
Vout =
R1 =
R2 =
I =
Vout =
Design a “divide by 2” voltage divider so that Vout = Vin / 2, where the resistances are in thousands of ohms. (2 points)
Figure 6: LTSpice dual voltage divider equivalent
Figure 6: LTSpice dual voltage divider equivalent
(a)
(a)
R3=
R4=
Use the 1.16V output from (a, b, and c) as the input to the “divide by 2” voltage divider from Question 8 (the output should be 0.58V). Putting the two “divide by 2 voltage dividers” as shown in Figure 6 where the R1 and R2 values are from question 7. Measure Vin, Vout, and I of the “divide by 2” voltage divider and fill out the following tables: (3 points each)
(a)
(a)
(b)
(b)
(c)
(c)
R1=
R1=
R1=
R2=
R2=
R2=
R3=
R3=
R3=
R4=
R4=
R4=
I=
I=
I=
Vin=
Vin=
Vin=
Vout=
Vout=
Vout=
Explain the trend: of voltage dividers a, b, and c, which was successfully “divided by 2”? Why didn’t the other sets work? What assumption in the voltage divider equations was violated that prevented the voltage divider circuit blocks from stacking? (3 points) ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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