Lab #2 Help Document

This help document will be structured as a walk-through of the lab. We will include instructions about how to write the report throughout this help document.

This lab will be completed in room 335 CTB.

You will need to partner up for this lab in groups of two.

Just as a reminder, when writing your lab report, remember to state what you did, how you did it, and why you did it. Include equations used and all calculations performed. Also, if the lab says to repeat the steps in a previous part, repeat all of the steps including the making of any calculations, analysis, graphs, or other requirements.

This lab will require the use of the following pieces of equipment:

DC power supply

DMM

Bread Board

3 Resistors:

Resistance Value in ohms (Ω) Color Bands

33 Ω Orange-orange-black

100 Ω Brown-black-brown

330 Ω Orange-orange-brown

There are 6 steps in this lab. It is best for this lab to do them in the order that they are written.

1. First measure the resistance of each of your resistors using the DMM. As you did in the previous lab, determine how close each resistor is to its rated value, and whether it is within its rated tolerance.

This part is relatively straight-forward. It’s the same set of steps performed for part 1 of the previous lab except that you use two fewer resistors this time. If you need to review how to make a resistance measurement or how to use a breadboard, please see the following section, else you can skip the next section:

How to measure Resistance using the DMM

To measure the resistance of a resistor, you only use the DMM (never have the DC power supply connected to a circuit when measuring resistance. Doing so can damage the DMM and will give incorrect readings). First configure the DMM for measuring resistance by placing the leads in the correct holes and selecting the resistance setting. Make sure the automatic unit resolution is on.

Connect the red lead to one of the resistor’s leads and the black lead to the other of the resistor’s leads. The reading on the screen is your resistance.

Back to Part 1

First, make and record your resistance values for your 3 resistors. Next, use the % difference equation to calculate how close each resistor is to it’s rated value. The equation is:

[(MV – RV)/RV] * 100 where

MV = Measured Value

RV = Rated Value

Remember to state whether each resistor falls within its rated tolerance. All of the resistors in the lab have gold bands, so they have ±5% tolerances. If the percent difference you found with your calculation is less than 5%, then your resistor is within tolerance.

Lab Report

For your lab report, you will need to record how you configured the DMM to measure resistance, how you measured the resistors using the DMM, the resistances that you measured, the percent difference equation and it’s components, your calculated percent difference values, and whether or not the resistors were within tolerance. Be sure to specify the units with all resistance values. You can use your resistance measurement descriptions from lab one (if they are complete) to describe how you made measurements. Remember that they need to describe completely how you set up the equipment and made the measurement. For example, to describe how you set up the DMM you can say:

“I configured the DMM to make voltage measurements,” and follow that with a picture or diagram of the DMM showing the red and black leads in the proper holes along with the screen on showing the units for resistance.

Then for the actual measurements, you could say something like:

“Measurements were taken as shown in this picture/diagram,” and then have a picture showing a resistor on a breadboard with the red lead of the DMM on one side and the black lead on the other. You could also use a written description, though image descriptions may be simpler to create especially if pictures are taken of the steps during the lab process. Regardless of whether you use images or written descriptions, ensure that the description is complete, meaning another person who hasn’t taken this lab and doesn’t know how to set up the equipment could use your description to make the same measurements. Also, keep digital copies of this and future lab reports in case the same measurement is made during a future lab. You can use the descriptions from this lab for those reports as well as long as they don’t have extra bits that need to be documented.

If measurements are made multiple times during a lab, you only have to describe the first measurement with the detail indicated above. All other measurements of the same type can refer to this description. For example, if you measure resistance in part 1 and part 6, you only have to describe the method of making the measurements and setting up the DMM in part 1. You can refer back to them in part 6. You do still need to include any measured values however for both parts.

As far as recording your data is concerned, include the following information:

Include all used equations. This part of the lab only had one, so include it:

[(MV – RV)/RV] * 100 where

MV = Measured Value

RV = Rated Value

This is an example of how you can record your data. You don’t have to do it this way as long as your recording includes all of the values/statements specified in the table below with their corresponding units.

Rated Value (ohms)

Measured Value (ohms)

Calculated % difference

Tolerance of resistor (%)

Is it within tolerance?

33 35.39 7.24 5 No

100 101.29 1.29 5 Yes

330 325.9 -1.24 5 Yes

2. With the DC power supply set to +5V, connect the 330Ω resistor and measure the current.

This part is like part 3 of the previous lab where you measured the DC current through 5 resistors, except that you are only measuring current not calculating expected current and you are only measuring it through the 330 ohm resistor in this case. The +5V setting on the DC power supply is constant throughout this lab so don’t change it after setting it the first time. You’ll also be doing current measurements from now on, so keep the DMM and DC power supply configured for DC current measurements. If you need to refresh on how to make DC current measurements, refer to the following. If not, skip it:

How to measure DC current through a resistor using the DC power supply and DMM

To measure the DC current through a resistor, you will need the DMM and the DC Power supply. First, make sure that the DC power supply is correctly configured and set the voltage to the value indicated in the lab using the rightmost voltage knob. Also configure the DMM for DC current measurement by placing the leads in the correct holes and selecting the DC current (not AC current) setting.

Connect the black leads of the DMM and the DC Power Supply together. Then connect the red lead of the DC Power supply to one lead of the resistor and the red lead from the DMM to the other lead of the resistor. This configuration places the DMM in series with the resistor allowing it to measure current.

Lab Report

Describe how you set up the DMM and DC power supply. Remember to state that you set the voltage to 5v.

Describe how you measured current through the resistor. Remember to make the descriptions complete such that someone else could read your report and replicate your experiment.

Show the current value that you measured. Remember to include the units for the measurement (mA in this case).

3. Now add the 100Ω resistor in parallel with the 330Ω resistor and measure the total current. Did the current go up or down? Calculate the expected current for the parallel combination and compare this value to the measured current. Were the results as expected?

This is where things start being new. For most of you, this is probably the first time you have made a parallel circuit, so I’ll explain a few things about them before moving on.

In a series circuit, current flows through each component in sequence. Say you have 3 resistors: R1, R2, and R3. The current will flow from the power supply, through R1, then through R2, then through R3, and finally back into the power supply. As the current flows through each resistor, a portion of the voltage is lost depending upon the size of the resistance (the bigger the resistance, the larger its share of the voltage drop). The voltage starts out at the voltage set on the power supply and ends as 0V after the current passes through the last resistor and returns to the power supply. The current remains constant throughout a series circuit and does not diminish at all between leaving and returning to the power supply. The total resistance of a series circuit is also equal to the addition of all of the resistances in that circuit. So, Rt would equal R1 + R2 + R3 and would continue in this manner if there were more resistors (Rt = R1 + R2 + R3 + …).

In a parallel circuit, current flows through each branch of the circuit simultaneously. A branch is simply a path that current can follow through. If you have 3 resistors in parallel with each other, then you have 3 different branches for current with a component (the resistor) on each branch.

Now let’s say you have 3 resistors: R1, R2, and R3. The current will flow from the power supply, through the three branches created by R1, R2, and R3 at the same time, and then return to the power supply. As the current flows, the voltage still goes from what it is set at on the power supply at the beginning of the circuit to 0V at the end when it returns to the power supply. This time, however, the voltage drop is the same for each branch and by extension each resistor meaning that the voltage drop across each resistor is 5V (voltage drops across each resistor are not added in a parallel circuit because the three resistors are basically treated like one resistor when they are in parallel). Also, unlike in a series circuit where the current through each component is the same as the current going through the circuit, the current going through parallel resistors gets split up depending on the resistance of each resistor. The amount of current that goes through each resistor is inversely proportional to the size of that resistor. In other words, if R1 and R2 are in parallel and R1 is 100 ohm but R2 is 10,000 ohm, then R2 will have much less current than R1 pass through it. This does not mean that current is lost. The current at the end of a parallel circuit is the same as the current at the beginning before going through the resistors. All that happens is that the current gets divided up when it hits the parallel resistors and added back together when it is through them. Also, unlike a series circuit, the total resistance of the circuit is found using this equation:

Rt = 1/[(1/R1) + (1/R2) + (1/R3) + …]

This has the effect of reducing the total resistance across the circuit. The resistance of the circuit will be less than that of the lowest value resistor.

For part 3 of the lab, the first thing that you do is add a 100 ohm resistor to the 330 ohm resistor in parallel. This is done using a breadboard by placing the 100 ohm resistor and the 330 ohm resistor such that one lead from each is in the same column of a breadboard. We’ve included the section on using the breadboard from the first help document if you need it. Pay attention to the part that shows how to set up a parallel circuit. If you don’t need this, skip down to the next section called Measuring DC current through a parallel circuit.

How to use a breadboard

A breadboard is a device that allows you to make circuits without soldering the leads. The breadboards used in this lab have 3 sets of connections composed of columns of connection holes. The first set is in columns of two holes. The second and third sets both contain columns of five holes.

The sets do not connect to each other so connections between sets are okay. Columns are not connected to each other through their connections while rows are. All connections within a column are connected together while all connections within a row are independent. Because of this, you NEVER place a component like a resistor such that two or more of its leads are in the same column. This will create a short circuit and can burn out the power supply. You can place leads from different components in the same row to connect them. For example, you can place one lead from a 100 ohm resistor and one lead from a 330 ohm resistor in the same row in order to connect them. If their other leads connect with different rows, the resistors will be connected in series. If their other leads connect

in the same row, the resistors are connected in parallel.

Measuring DC current through a parallel circuit

This is not as complicated as it may sound. After setting up your two resistors in parallel simply connect the red lead from the DC power supply to one lead of the 330 ohm resistor and connect the red lead from the DMM to the other lead of the 330 ohm resistor (your DMM and DC power supply should already be configured for DC current measurement and the two black leads from both of them should be connected unless you changed something during the lab). The reading on your DMM is the current through the two parallel resistors.

Something you should know is that you can take the red leads of the DMM and DC power supply off the 330 ohm resistor and connect them to opposite leads of the 100 ohm resistor instead. You will get the exact same measurement as when the red leads were connected to the 330 ohm resistor. If you added a third resistor in parallel and measured off of both of its sides, you would also get the same reading as if you measured from the 330 ohm or 100 ohm. This is because the DMM is measuring the resistance of the parallel circuit in all cases. In fact, as long as one red lead is on one side and the other is on the other side (of the resistors that is) you can measure between any pair of the resistors’ leads and get the same thing. Left side 330 ohm with Right side 100 ohm, left 33 ohm with right 330 ohm, and any other combination will all yield the same result. Think of it like water flowing through a pipe. In series, if you add a thinner pipe to the chain, water can’t flow through faster than what the thinnest pipe will allow. If you are adding pipes in parallel, however, each added pipe increases the amount of water that can flow through and water will flow through all 3 regardless of where the inputs and outputs are.

Based on this measurement and the measurement from part 2, was this measurement a higher or lower current? Is that what you would have expected? When you’re done measuring and recording the current through these two parallel resistors, move on to the next part.

Calculating expected DC current through a parallel circuit

To calculate the current through a DC circuit, you will need the following equations:

I = V/R which is ohm’s law and

Rt = 1/[(1/R1) + (1/R2) + (1/R3) + …] which is the equation for finding the total resistance in a parallel circuit.

All you have to do is find the total resistance and use that as the value for R in ohm’s law along with the voltage your power supply is set to (which should still be +5V at this point) and you get the current through the circuit.

Lab Report

For this part of the lab report, include how you set up a parallel circuit with the two resistors (can use a picture for this). Also specify how you measured the current through the parallel circuit with the leads of the DMM and Power Supply (can use a picture for this as well). You don’t need to describe how you set up the DMM and DC Power supply for a current measurement since you did this for part 2, but you do need to refer to that setup.

You need to include the measurement for current through the two parallel resistors and it’s units.

You need to state whether the current measurement for the two resistors in parallel went up or down from the current through the single resistor in part 2.

You need to include the equations you used to find the expected current through the parallel circuit. You used:

I = V/R ohm’s law and

Rt = 1/[(1/R1) + (1/R2) + (1/R3) + ] total resistance in a parallel circuit

So you need to include both of these as well as the number that you plugged into their variables. You need to indicate which numbers went where either by showing a calculation or labeling the values you used in the equation according to their parts. Example:

For each equation, either show:

Rt = 1/[(1/330 ohms) + (1/100 ohms)] = (show numeric answer here) ohms

Or

Rt = 1/[(1/R1) + (1/R2) + (1/R3) + ]

R1 = 330 ohmsR2 = 100 ohmsRt = (show numeric answer here) ohms

You need to compare the calculated current to the measured current and explain any differences that you see between the two values.

You need to state whether the results (meaning the measured and calculated current values) were expected and explain why you think that is the case. Hint: remember earlier how current in an electric wire was related to water flowing through a pipe, well what happens to the flow of water when you increase the number of pipes that the water is going through in parallel?

4. Now add the 33Ω resistor in parallel with both the 330Ω and the 100Ω resistors, and measure the total current. Did the current go up or down? Calculate the expected current for the complete parallel combination of three resistors and compare this value to the measured current. Were the results as expected?

This part is exactly like part 3 except that you add an additional resistor in parallel. Remember when you measure the current across the circuit to place the red leads of the DMM and DC power supply on opposite sides of the same resistor or you will either get the wrong reading or short out the power supply.

If you found that the expected current went up from parts 2 and 3 when you had 1 resistor and then 2 resistors in parallel, don’t worry you probably did it right. In a parallel circuit, the total resistance cannot be greater than the resistance of the smallest resistor. Since the smallest resistor in this lab is 33 ohms, you’re Rt can’t be larger than 33 ohms. Smaller resistance but the same voltage as the other tests means more current through this circuit.

Now, calculate the expected current through the circuit using the same method as described in part 3.

Lab Report

For this part of the lab report, you need to refer to parts 2 and 3 for how you set up the DMM/Power supply and for how you measured the circuit.

You need to include your measured current value through the parallel circuit including its units (mA).

You need to state whether the measured current through the three parallel resistors went up or down relative to the previous two circuits.

You need to refer to the equations used in part 3 and show the values that would be used in them for part 4. Also show the calculated current value.

You need to compare the calculated current to the measured current and explain any differences that you see between the two values.

You need to state whether the results you got were expected and why.

5. Calculate the expected current in each of the three branches of the above circuit, using the current divider method or using Ohm’s law. Measure the branch currents and compare to the calculated values.

For this part, you will be dealing with branches of parallel circuits. Series circuits do not have branches because current flows in one path through all of the circuit components. In parallel circuits, current flows through several paths simultaneously. Different paths within a parallel circuit are called branches. A branch can have one or more components within it and all components within a branch are in series with each other. This means that if you have more than one resistor in a branch, the resistance of that branch will be equal to the sum of the resistances of the resistors in that branch.

How to calculate the expected current through branches

For the sake of simplicity, we’ll show you how to calculate the current across each branch using ohm’s law. We do this because we know what the voltage is (you would use the current divider rule if you did not know what the voltage was), you are or should be familiar with ohm’s law, and it’s just easier this way in my opinion.

To calculate the current across each branch of a parallel circuit, you simply plug the values you have into ohm’s law. For example: say you have 3 resistors with values 100 ohm, 200 ohm, and 300 ohm and they are all in parallel with each resistor on its own branch. The voltage being input is 5V (remember that since this is a parallel circuit, the voltage drop across all branches is the same and since each resistor is on its own branch, the voltage drop across all resistors is the same by extension.) Since each branch has only one resistor, the resistance of that resistor is the resistance of the branch. As such, all you have to do is plug that resistance and the voltage of 5V into ohm’s law to find the current through that branch.

Example:

Branch 1 has 100 ohm resistor

I = V/R 5V/100 ohms = 50 mA

Branch 2 has 200 ohm resistor

I = V/R 5V/200 ohms = 25 mA Branch 3 has 300 ohm resistor

I = V/R 5V/300 ohms = 16.667 mA

Measuring current through an individual branch

When you have calculated the expected branch currents, you will need to measure the current through each branch. To do this, first configure your DMM for DC current measurements and connect the black leads of your DMM and DC power supply. Now take one of the red leads from either the DMM or DC power supply and connect it to one side of a branch (since these branches are only 1 resistor large, just connect the lead to one of the resistor leads). Before connecting the other red lead to the other side of the branch, you will need to isolate that branch from the circuit. You do that by removing the resistor lead that is not connected to a red lead from the breadboard. When this is done, clip the other red lead to it. The measurement on your DMM is the current through that branch.

Lab Report

For this part of the lab, you need to show the equations you used to calculate the branch currents through each resistor. Again, show the equation and the values used in it:

I = V/R

Resistance (ohms) Voltage (volts) Current (mA)#### #### ######## #### ######## #### ####

Show the measured branch values for each resistor (include units).

Compare the measured values to the calculated values. Are they higher, lower, the same? If different, why?

6. To observe the relationship described by the power formula P = E²/R: Calculate the power being dissipated by each resistor in step 5. Feel the heat being dissipated by each resistor and determine if it agrees in rank as you would expect for each resistor. (Which one is the hottest? Which is the coolest? Is this as you expected?)

How to calculate expected power dissipation

For the first step in this part of the lab, all you have to do is calculate the expected power that will be dissipated by each resistor from part 5 of the lab. You can do this by using the equation:

P = E²/R

where P is the power dissipated by the resistor, E is the Voltage (equation can also be written as P = V²/R), and R is the rated resistance of the resistor. The voltage is the same 5V that the power supply has been set to because this is a parallel circuit, so the voltage across each resistor will be the same as the input voltage to the circuit.

Example: Find the power dissipation across a 100 ohm resistor with 5V input.

P = E²/R 5V^2/100ohm = 250 mW or 0.25 W

The unit for power dissipation is the watt represented by W or milliwatt represented by mW.

How to feel the heat dissipation

This section is relatively self-explanatory. All you have to do is connect the 3 resistors in parallel again and connect just power supply to them by connecting the black lead to one side of the circuit and the red lead to the other side.

Once the circuit is connected to the power supply, take you finger and touch it to each resistor and determine the order from greatest to least for which resistor puts off the most heat. The heat output is directly proportional to that resistor’s power dissipation. BE WARNED!!! Some of the resistors may get very hot to the touch. Don’t leave your finger on them too long or you might burn yourself. Also, when you are done ranking them, turn off the power supply so that the resistors don’t overheat.

Lab Report

State that you set the DC Power Supply to 5v and connected it directly to the parallel circuit of the 3 resistors without the DMM.

Show the calculated values for the power dissipated by each resistor. Include the equation and a table showing the values according to which variable they occupy in the equation (remember to include units). Example:

P = E^2/R

Resistance (ohms) Voltage (volts) Power (W)#### #### ######## #### ######## #### ####

Show the ranking of your resistors according to which one puts off the most heat. State whether the heat dissipated by the resistors ranks the way you would have expected and why.