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Lab Report Experiment 3: Voltage and

Current Division Abstract— The objective of this lab is to observe and compare how when

The files that were saved included the input voltage and the

resistors are set in parallel, they behave similar to current dividers and how when resistors are set in series they act like voltage dividers. In this lab, we were able to simulate for the Voltage Division and Current Division in MultiSim and get to compare the graphs to understand that Kirchhoff’s Law is consistent. In this experiment, we could see how parallel and series resistances work and how we can get an accurate measurement of them when we want to know the voltage or current going across each of them, and how voltage divides in a series circuit while current divides in a parallel circuit.

Vout voltage across the 33k ohm resistor. The next circuit we analyze is the parallel circuit, consisting of three resistors, one in series with the source voltage and the other two resistors in parallel. Fig.2 shows the MultiSim circuit that we use for both the MultiSim and LabVIEW data.

INTRODUCTION

In this lab, we look at the ways in which voltage and current is divided in series and parallel circuits, respectively. We’ll first look at simulated circuits in MultiSim for both series and parallel circuits and then compare that data to our measured values in LabVIEW using MatLAB analysis. The main things that we are looking to find is how the voltages across resistors in a series circuit add up to the input (or source) voltage and how the currents across resistors in a parallel circuit add up to the input (or source) current going into the initial branch.

I. MULTISIM ANALYSIS OF BOTH SERIES AND PARALLEL

Figure 2. Parallel Circuit for MultiSim and LabVIEW Analysis

We make the same measurements for the parallel circuit in unit steps of 0.1 V but this time we measure three currents going through the three resistors, the current through R1 and the currents going through R2 and R3. We also take the step voltage across the source, totaling four files.

CIRCUITS

For this portion of the lab, we start with our series circuit using 2 resistors and a DC voltage source. Fig.1 on the bottom shows where we take our measurements from and what value resistors we use.

II. LABVIEW ANALYSIS OF BOTH SERIES AND PARALLEL CIRCUITS So far, we’ve only had data for MultiSim which is the ideal voltages and currents for our circuits. Now we build the actual circuits on the ProtoBoard and take down the same readings we did before in MultiSim. The first measurement we take down are the ones for the resistors. We also calculate the error between the color-coded values and the measured values using the equation given by:

%"#$$%$ = 100% ∗ Figure 1. Series circuit for MultiSim and LabVIEW analysis

We took step readings (of 0.1 V steps) of the voltages of the MultiSim circuits of both the Vout after the 15k ohm resistor and the input voltage across the source. We would solve for the voltage across R1 by subtracting the source voltage later on.

Color Coded Value (ohms)

*+,-.$+/ − 1ℎ+%$3 1ℎ+%$3

Measured Error (%) Resistance (ohms) Series R1 15k 14.835k 1.1 Series R2 33k 32.943k 0.173 Parallel R1 1k 982 1.8 Parallel R2 22k 21.924k 0.345 Parallel R3 10k 9.867k 1.33 Table 1. Color Coded and Measured Values for the Resistances

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A) Series circuit Now we build the series circuit from Figure 1 on the ProtoBoard, set the voltage source to 5 V and check the voltages as well as the errors across the voltages. Table 2 gives these values.

R1 R2

Pre-Lab Value Measured (V) Error (%) (V) 1.5625 1.549 0.864 3.4375 3.4437 0.1804 Table 2. Pre-Lab and Measured Voltages and Errors Associated

Now we can take the same readings we had taken during our MultiSim analysis. We do the same thing and sweep the input voltage in 0.1 V steps from 0 to 5 V and do it for both resistors and save the .txt file for MatLAB analysis later. The next step is the parallel circuit. We build it on the ProtoBoard and instead of measuring the voltages, we now measure the currents across all the resistors. The lab required that we take down all the current measurements by hand in

Figure 3. Resistor Voltages vs. Input Voltage

Notice that if you were to add the resistor voltages, you will get the input voltage which shows the property of series circuits that the voltage across resistors in series will add up to the input voltage (or Kirchhoff’s voltage law that the voltage around a loop equals zero).

regular 1V intervals. Table 3 shows the measured and calculated currents for the parallel circuit. Table 4 shows the error for the same measured and calculated currents. V(s) (V)

1 2 3 4 5

is (mA) Calculated Measured

i2 (mA) Calculated Measured

i3 (mA) Calculated Measured

0.1270 0.1282 0.0397 1 0.1270 0.1282 0.2540 0.2566 0.0794 2 0.2540 0.2566 0.38095 0.3851 0.1190 3 0.38095 0.3851 0.5079 0.5136 0.1587 4 0.5079 0.5136 0.6349 0.6424 0.1984 5 0.6349 0.6424 Table 3. Measured and Calculated Currents of the Parallel Circuit

V(s) (V)

is i2 i3 Error (%) Error (%) Error (%) 1 0.945 0.503 1.145 2 1.024 0.630 1.145 3 1.076 0.916 1.260 4 1.123 0.090 1.317 5 1.181 0.857 1.283 Table 4. Error Between the Measured and Calculated Currents

Going back to Part 1 of our lab, the lab required that we create three graphs from our MultiSim data. All three graphs are shown on the next page.

Figure 4. Branch Currents vs. Input Current

B) Parallel circuit This graph is for the parallel circuit and again, you’ll see that the branch currents always add up to the input current. Just for reassurance, we add up the branch currents and graph it against the input current.

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Figure 7. Summation of Measured Voltages against the Input Source Voltage

Yet again we see a near 1 slope showing that the summation Figure 5. Sum of Branch Currents vs. Input Current

Notice again that the sum of the currents almost completely add up to the input current. This is shown by the nearly slope of 1 from this graph. We were then asked to compare the MultiSim and LabVIEW data for our series circuit.

(or Kirchhoff’s Voltage) law holds for series circuits.

III. MULTISIM AND LABVIEW COMPARISON The next graph shows the parallel circuit and compares both the measured and MultiSim data altogether in one graph.

Figure 8. Separate Measured and MultiSim Data for Currents Figure 6. Comparison of MultiSim and LabVIEW data

We see very similar values for both MultiSim and LabVIEW data and again they nearly add up to the input voltage but just to make sure, we add up the measured voltages across the resistors and compare it to the input source voltage in Figure 7.

Again, we can see that the measured and MultiSim data overlap closely so that our measured and ideal values are close (very little error) and that the currents do nearly add up to the source current. But, again, just to make sure, we graph the summation of the currents against the source current to get the graph below.

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out that not all materials behave that way. There are several materials that we know of that will not follow this linear property and thus Ohm’s law isn’t much of a universal law as it is a guideline.

VI. REFERENCES

[1] Electrical Engineering Laboratory I, CCNY Departent of Electrical Engineering, New York, NY Spring 2016

Figure 9. Summation Currents against Source Current

Again, a near perfect overlap shows near zero error and a near 1 slope shows that Kirchhoff’s current law holds for parallel circuits.

IV.

ANALYSIS

Seeing as how Ohm’s law only refers to (or includes) conductors as having this linearity proportion, evidently it cannot be considered a universal “law” such as gravitation. While all mass has a gravitational pull associated to it, not all materials have a linear proportion to the amount of current going through it. While the resistors we used in the lab seemed to be linearly proportional to the voltages we had put across it, if we were given an unknown resistor (which may or may not have the same properties), we wouldn’t be able to make the calculation without first measuring (perhaps by the step function of the voltage) the current and seeing whether it follows Ohm’s “Law”. So no, it is not a universal law and we wouldn’t be able to figure out the current by simply measuring the resistance and voltage and then assuming that the resistor has linear properties associated with it.

V. CONCLUSION What we could gather from this lab is that for the most part, Kirchhoff’s Voltage and Current law hold for the circuits we had created in the lab. Whether it was through MultiSim or LabVIEW, our values came very close to each other with errors that were very small (many of them being less than 1%). We could verify that the materials that we were using had linear properties so that we could use Ohm’s law but we also figured...