Ohm's Law and Circuits

photo showing general lab setup of powersupply, voltmeter and resistors

In this lab we will look at the current through and voltage across resistors in series and parallel circuits. According to Ohm's Law, the current through a resistor is proportional to the voltage across it:

V = I R

We will look at three different circuits, one in series, one in parallel and one "mixed". By measuring the current through and voltage across each resistor we will confirm our rules for adding resistors.

Pick three resistors, measure their resistances and record these values in your lab notebook.

A) Series Circuit
In your notebook, diagram a series circuit with the resistors you picked.

Set your power supply to ten volts.

Turn off your power supply. Your instructor will tell you how breadboards work, place the three resistors in series. Knowing the values of the resistances, predict in your notebook the values of the current through and voltages across each resistor.

Place DMM in series with the circuit, between your third resistor and the power supply. See figure 1. Set your DMM to read current. Have your instructor inspect your circuit before you turn on the power. Turn on the power supply and measure the current that flows out of R3. Record this (with error) in your lab book.

diagram shows a battery with a wire coming out of it.  The wire goes into
a resistor, which goes into another resistor, which in turn goes into a third resistor.  After the last resistor is a current meter, and
this feeds into the back end of the battery
Figure 1 - Measuring Current in a Series Circuit

Repeat and measure for R2, R1 and the current flowing out of the power supply. Remember to turn off the power before changing the circuit!

The next step is to measure the voltage across each resistor. To do this we need to set the DMM to voltage and wire it parallel to the element that we are measuring. Measure the voltage from the power supply and the across each resistor. Record these values in your lab notebook.

B) Parallel Circuit
In your notebook diagram a parallel circuit with your resistors.

Wire up this circuit. Have your lab instructor inspect it before you turn on the power. Again, predict the current through and voltage across each resistor.

Measure the current through each resistor; this will involve setting the DMM to current and putting it in series with what you are measuring. See figure 2; the solid position gives the total current, the dashed gives the current through resistor 1. Measure the voltage across each of the resistors. Record all of these values in your notebook.

Warning: You should think about the size of your resistors when you do this, keeping in mind that the resistors we use in class are rated for 1/4 watt of power.

battery has a wire coming out of it.  The wire splits into
three branches, each with a resistor.  The three branches then reconnect.  If you measure the current before the branches
reconnect, you get the current going through an individual resistor.  If after, then you get the total current.
Figure 2 - Measuring Current in a Parallel Circuit

C) "Mixed" Circuit
Build a circuit that features two of your resistors in parallel, and the third resistor is series with this pair. Diagram the circuit in your notebook and predict the current and voltage for each resistor. Once this has been done, measure the current and voltage for each resistor. How well do they agree with your predictions?

D) Internal Resistance of the Function Generator
If you take a close look at your function generator, it says "50Ω OUT" by the outputs. What this means is that the power supply acts as if it were a voltage in series with a 50Ω resistor. For circuits that have large resistances, this can usually be ignored, but at times it needs to be accounted for. In this section we will verify the internal resistance.

Plug in your function generator, set it to 50Hz sine waves, and measure the voltage with a DMM. Make sure that the DMM is set to measure AC voltages. When you measure the voltage with the voltmeter, due to the details of the internal construction of the DMM, you are measuring the voltage of the function generator (in practice we can treat the DMM as if it was a very large resistor, and hence ignore the internal resistance). Next connect a 50Ω resistor to the function generator. You will find that the voltage across the new resistor is roughly half the previously measured voltage. Draw a ciruit diagram with the internal resistance in series with your "load" resistor. Use your voltage measurements and the resistance of the load to verify that the internal resistance of the function generator is what it says it is.

E) Light Bulb
Make a series circuit with a 100 ohm resistor and a light bulb. Incrementally increase the voltage to the circuit and measure the current through the circuit by observing the voltage across a resistor. Since we are looking for the resistance of the lightbulb, we'll need to know the voltage across the bulb, which should be the voltage of the power supply minus the voltage across the resistor. Plot the current as a function of voltage across the lightbulb, keeping an eye on your intercepts. What should it look like? What does it look like? What does this tell you about the lightbulb?

In your conclusion you should compare your measured results to the expected values derived from the rules we have for adding resistors in series and parallel. Comment on the lightbulb results. In general, does the DMM change the results you measure? Why must it be placed in series for a current measurement and in parallel for a voltage measurement?

Pre-Lab: Ohm's Law
This week in lab we will measure a series circuit, a parallel circuit and a "mixed" circuit. Prior to lab you should play with the DC Circuit Construction Kit.

Needless to say, build a series circuit with two resistors, and measure the voltage across and current through each circuit element. Do the same for parallel and mixed circuits (the mixed case will need three resistors). For the values of the resistors, use the month, day (and for mixed, year) of your birth. Print out copies of the results, and on the hard copies write down the math that shows why your results are correct.