Lab D06: Combinations of Resistances

(2/04/97)

b. You should see a trend in how the measured equivalent resistance relates to the individual resistance values. From the trend you observed, write down a sentence describing the trend (qualitative words only, no math). Your sentence should be something like: "As the number of resistors in a series increases, the equivalent resistance of the combination...."

c. Write a general formula for the equivalent resistance (R_EQs) of N resistors (R₁, R₂, R₃,...R_N) in series. Make sure your formula obeys the sentence you wrote above.

3) a. To test your formula, put your remaining two resistors in series. BEFORE you do any measuring PREDICT/CALCULATE the equivalent resistance of these two resistors in series.

b. Now measure the equivalent resistance of the series combination. Did your expression for the equivalent resistance of two resistors in series work for this new combination? Try some other new series combinations to convince yourself--organize and clearly document your work.

4) Explain why the equivalent resistance is larger than any individual resistance in the series. Consider that all of the resistors are made of the same material.

Part B: Exploring Resistances in Parallel

1) a. Measure and record the equivalent resistance of two, three, and four different resistors strung together as symbolically shown in the three examples below (called resistors in parallel). Use R₂-R₅ to make these combinations. Use the breadboard to put the resistors in parallel--do not twist the resistor wires together. Be sure to grasp the resistor wires right up against the breadboard when inserting and removing the resistors on the board or the wires will kink. DO NOT MANGLE THE RESISTOR WIRES!

Click here for Picture

b. Again, you should see a trend in the measured resistance values. From the trend you observed, write down a sentence describing the trend (qualitative words only, no math). Your sentence should be something like: "As the number of resistors in parallel increases, the equivalent resistance of the combination...." Write a second full sentence describing how the equivalent resistance always compares to the smallest individual resistance in the parallel combination.

c. Once your descriptive sentences are done, write a general formula for the equivalent resistance (R_EQp) of N resistors (R₁, R₂, R₃,...R_N) in parallel. Make sure your formula obeys the sentences you wrote above. Make sure that your formula yields R_EQp in ohms. You should find this formula more challenging than that for series combinations. However, try to keep your formula as simple as possible.

2) a. To test your formula, put your remaining two resistors (R₁ and R₆) in parallel. BEFORE you do any measuring PREDICT/CALCULATE the equivalent resistance of these two resistors in parallel.

b. Now measure the equivalent resistance of the parallel combination. Did your expression for the equivalent resistance of two resistors in parallel work for this new combination? Try some other new parallel combinations to convince yourself--organize and clearly document your work. If you find your formula isn't working well, write another and test again.

3) Explain why the equivalent resistance is smaller than any individual resistance in the parallel combination. Consider that all of the resistors are made of the same material.

_{Part C: A Test of What You Learned}

Obtain three resistors of equal value and record that resistance value. Use these three resistors to construct four different combinations, each yielding a unique equivalent resistance value. Draw the resistor pattern of each different combination; predict/calculate the equivalent resistance of each pattern (work carefully and neatly); then measure the equivalent resistance directly with the multimeter and compare (% diff.) to the calculated values.