In the next experiments you will examine how the arrangement of resistors in a circuit leads to a total resistance for the circuit.

Question

Part B1: Resistors Arranged in Series

Step 1: Create two more resistors

Try to make a second and third resistor that match your first one - using the same dimensions (1 cm x 5 cm) and covering the card stock with same amount of graphite.

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Step 2: Series connection

Using two more binder clips and a piece of aluminum foil, connect the one of the new resistors to your existing circuit from Part A, by connecting the two resistors in a line as shown.

Warning: Make sure that the four binder clips do not touch each other.

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Step 3: Contact LED to resistors

Compare the brightness of the LED when it is in contact with the 2nd resistor (upper picture) to when it's in contact with only the 1st resistor (lower picture). Note that only the leg of the LED is being moved in these measurements (i.e. do not modify the rest of the circuit between these two measurements).

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Step 4: Connect the third resistor in series

Add the third resistor in series, using the remaining two binder clips and a piece of aluminum foil. Compare the brightness of the LED when it is in contact with the 3rd resistor.

Observations:

When you have assembled your 3-resistor series configuration, take a picture of your circuit (you will be asked to submit this at the end of the lab).

Note the brightness of the LED when connected to the 1st vs 2nd vs 3rd resistors. Record your observations and comment on how the combination of resistors acts to produce a total resistance.

Part B2: Resistors Arranged in Parallel

Now that we have assembled a circuit with resistors in parallel, create a circuit in which resistors are arranged in a parallel combination. The circuit diagram below shows a configuration with two resistors in parallel. Based on your use of binder clips and aluminum foil, it is possible to also create a circuit with three resistors arranged in parallel, and may help to demonstrate the effects of parallel combinations.

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Caution:

Make sure that the four binder clips do not touch each other. As with previous circuits, it is important to make sure to avoid contact between binder clips which will alter the pathways available for current to flow.

Observations:

When you have assembled your parallel configuration, take a picture of your circuit (you will be asked to submit this at the end of the lab).

Note the brightness of the LED when 1, 2 (and 3?) resistors are connected in parallel. Record your observations and comment on how the combination of resistors acts to produce a total resistance.
Question 2 (1 point)
Consider the three circuits that you have created:

Circuit 1: Single resistor (total resistance R1)

Circuit 2: Three resistors in series (total resistance R2)

Circuit 3: Three resistors in parallel (total resistance R3)

Rank these in terms of their total resistance, from least to greatest.
Question 2 options:

R1 < R2 < R3

R2 < R3 < R1

R2 < R1 < R3

R3 < R1 < R2

R3 < R2 < R1

R1 < R3 < R2

Answer 1

To determine the correct ranking of the total resistances \( R1 \), \( R2 \), and \( R3 \) for the circuits you created, we need to remember the fundamental rules for combining resistors in series and parallel:

1. Series Resistors: The total resistance of resistors in series is the sum of their resistances: \[ R_{\text{series}} = R_1 + R_2 + R_3 \] Thus, the total resistance \( R2 \) (with 3 resistors in series) will be higher than the resistance of any individual resistor.

2. Parallel Resistors: The total resistance of resistors in parallel is found using the reciprocal formula: \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \] This means that the total resistance \( R3 \) (with 3 resistors in parallel) will be lower than the resistance of any individual resistor and certainly lower than the total resistance of resistors in series.

Given these rules, we can analyze the three circuits:

• Circuit 1 (Single Resistor, \( R1 \)): This has the lowest resistance.
• Circuit 2 (Three Resistors in Series, \( R2 \)): This is the sum of three resistances and will be the highest.
• Circuit 3 (Three Resistors in Parallel, \( R3 \)): This will be lower than the resistance of any individual resistor (thus lower than \( R1 \)).

Based on these evaluations, the ranking from least to greatest resistance is: \[ R3 < R1 < R2 \]

So the correct option for your question would be: R3 < R1 < R2