Electricity and Magnetism Module 4
Student Guide

 

Note: each time you are finished with a circuit we ask that you disconnect all wires, so that the next circuit you investigate starts with a “blank slate”.

Concepts of This Module

• Resistance

• Ohm’s Law

• Series and Parallel Circuits

• Electric Power

 

Activity 1

 

Consider the circuit shown to the right using three of the supplied light bulbs labeled 6V 6W. The label means the bulb is rated for 6 watts at 6 volts

1. Without doing any calculations, predict what will happen to the brightness/dimness of Bulb 1 when the switch is closed. Explain your prediction without equations.

2. Wire the circuit and check your prediction. Was your prediction correct? If not, describe what happened.

3. How does the brightness of Bulb 2 change when the switch is opened and closed?

4. With the switch closed, how does the brightness of Bulbs 2 and 3 compare?

5. Measure the voltage drop over the bulbs for when the switch is open and when the switch is closed (ie. 6 measurements in total, two for each bulb). How do these measurements relate to your observations in questions C and D? Do they explain any of your observations, and if so how?

 

 

Activity 2

 

Set up a simple circuit with one battery and one 6V 6W light bulb, and use two multimeters: one to measure the current going through the bulb, and one to measure the voltage drop across the bulb.  Below is a circuit diagram of how you might do this, where A means a multimeter set in "Ammeter mode", and V means a multimeter set in "Voltmeter mode".  This is sometimes called the "four point measurement" technique ( https://en.wikipedia.org/wiki/Four-terminal_sensing ).  Use Ohm's Law and your measurements of \(\Delta V\)  and \(I\) to compute \(R\).  What is the resistance of a single 6V 6W light bulb (include uncertainty)?  You have three 6V6W bulbs, do they all have the same resistance, and if so, to what uncertainty?   

[Note that the current in the circuit may be over 300 mA. If so, the inputs to the ammeter should be connected to COM and 10A sockets.]

Activity 3

What is the resistance of the light bulb labeled 6V 1W ?   Compare the brightness and the resistance properties to those of the 6V 6W light bulb.

 

Activity 4

 

You are supplied with two short yellow banana plugs. Use the two yellow banana plugs to connect two of the 6V 6W light bulbs together in parallel and place the combination in a circuit with an ammeter and the battery. Below is a circuit diagram.

 

[Note that the current in the circuit may be over 300 mA. If so, the inputs to the ammeter should be connected to COM and 10A sockets.]

1. The two yellow banana plugs are the segments between points A1 and A2 and between B1 and B2. When you measure the voltage across the two light bulbs, does it matter whether you connect the voltmeter across A1 and B1, across A2 and B2, across A1 and B2, or across A2 and B1? Why?

2. Assume the resistance of each light bulb is the same value \(R_1\), which is the average of what you measured in Activity 2 above.  What is the predicted effective resistance of the two identical bulbs in parallel [you may need to consult your textbook or TA]?  Use two multimeters to measure the total current through the pair and the voltage drop across the pair, then use Ohm's Law and determine the measured effective resistance of the two identical bulbs in parallel,  and compare with your prediction. 

3. Use the same circuit shown above, but replace one of the 6V 6W bulbs with a 6V 1W bulb.  You now have two resistors in parallel, \(R_1\) and \(R_2\).  Based on your individual measurements of resistance in Activities 2 and 3, what is the predicted effective resistance of the two different bulbs in parallel?  Use two multimeters to measure the total current through the pair and the voltage drop across the pair, then use Ohm's Law to determine the measured effective resistance of the two different bulbs in parallel,  and compare with your prediction.

Activity 5

 

Use one of the short wires to connect two of the 6V 6W light bulbs in series, and place the combination in a circuit with an ammeter and the battery, as shown.

 

 

 

 

 

 

 

 

 

1. How does the brightness of the light bulbs compare to their brightness in the parallel circuit of the previous Activity?

2. Assume the resistance of each light bulb is the same value \(R_1\), which is the average of what you measured in Activity 2 above.  What is the predicted effective resistance of the two identical bulbs in series [you may need to consult your textbook or TA]? Use two multimeters to measure the total current through the pair and the voltage drop across the pair, then use Ohm's Law and determine the measured effective resistance of the two identical bulbs in series, and compare with your prediction.  Note that, unfortunately, the resistivity of the metal tungsten filament in the bulb is a function of temperature.  That means that if the voltage across an individual light bulb is changed, it may change the power being consumed and therefore its running temperature.  So it's possible that the resistance of the two bulbs wired in series is different than what you measured before!  Use your multimeters and Ohm's Law to check the resistances of the individual bulbs while wired in the series circuit, and, if they are different, correct your prediction.  Does this prediction come closer to the measured effective resistance?

3.  Use the same circuit shown above, but replace one of the 6V 6W bulbs with a 6V 1W bulb.  You now have two resistors in series, \(R_1\) and \(R_2\).  Again, using the old values of R_1 and R_2, what is the predicted effective resistance of the two different bulbs in series?  Use two multimeters to measure the total current through the pair and the voltage drop across the pair, then use Ohm's Law to determine a measured effective resistance of the two different bulbs in series,  and compare with your prediction.  Probably the running temperatures are different again, so measure the new individual resistances and update your prediction.   

4. How do the brightnesses of the 6V6W bulb and the 6V1W bulbs compare now that they are wired in series? Which is the brightest, and why?  Compare this with when the different bulbs were wired in parallel.

 

Activity 6

 

The diagram to the right has 6 different resistors that are connected by perfect wires. Describe how you might calculate the total effective resistance between points A and B. You may find it helpful to re-draw the diagram with the resistors and wires laid out in a more standard fashion. 
 

 

Activity 7

 

So far we have been treating the battery as perfect: it delivers a constant voltage in all circuits. Real batteries have a non-zero resistance, and we can represent the internal resistance r of the battery as shown. Now the battery symbol represents a perfect battery in series with the internal resistance of the real battery. Call the voltage of the perfect battery .¹

 

Describe how the voltage delivered by a real battery ∆V_real varies with the current I being drawn from it.  Can you measure the internal resistance of the actual battery on your table?

 

 

 

Activity 8

 

The earth contains minerals and moisture, which means that it is a usually a good conductor of electricity. Therefore, it is possible to wire a light bulb using the earth as the return path for the current: in the figure two metal rods have been stuck into the ground and connected to the circuit as shown.

The symbol for a connection to ground is:

 

 

 

Therefore we can represent the above circuit as shown to the right.

 

 

1. The resistance of your arm from your palm to your shoulder is about 150 Ω. Estimate/measure the resistance of your body from your palm to the soles of your feet.
    

2. An electric fence consists of a single wire connected to one terminal of a voltage source; the other terminal of the voltage source is connected to ground. If the voltage ∆V is 120 volts and you touch the fence with your hand while standing on the ground in your bare feet, what is the number of watts your body will absorb while in contact with the wire?

 

 

 

 

 

 

 

 

 

 

 

 

This Guide was written in November 2007 by David M. Harrison, Dept. of Physics, Univ. of Toronto.  Updated by Jason Harlow in February 2025.

 

The cartoon of the person touching an electric fence is from the Glasgow Digital Library: http://gdl.cdlr.strath.ac.uk/hewwat/hewwat0206.htm

 

Last revision: March 26, 2011.