Interpreting your observations

Read this section once you have completed the experimental tasks.

Task 1 – resistors in series explained

In this task you first examined each resistor individually – for example, you may have noted that when the 1 MΩ resistor was placed in the circuit with a 9 V battery, the recorded current was approximately 9 µA when the circuit was turned on (though this will vary slightly depending on the tolerance of the selected resistor). The second part of this task was to examine the effect of resitors in series on current follow. Let’s continue with the 1 MΩ resistor selection – you may have noted that two 1 MΩ resistors in series only allowed approximately 4.5 µA to flow in the system.

How much current would flow in an electrical circuit with a 9 V battery and a single 2 MΩ resistor? (Remember that 1 MΩ is 1 million ohms.)

Using Ohm’s law I =V/R, the current flowing through circuit will be 4.5 µA. So two 1 MΩ resistors in series behave in the same way as a single 2 MΩ resistor.

Resistors in series combine together, for example, if you had a circuit with a 2 Ω resistor and a 8 Ω resistor in series, their combined series resistance is 2 Ω + 8 Ω = 10 Ω.

Task 2 – resistors in parallel explained

Resistors in parallel behave differently to those in series. For this worked example, we will use 5 Ω resistors in an electrical circuit with a 9 V battery. A single 5 Ω resistor will produce a current of approximately 1.8 A and two 5 Ω resistors in series will produce a current of approximately 900 mA. Whereas two 5 Ω resistors in parallel produce a current of 3.6 A.

Let’s summarise:

You might have been surprised to learn that two resistors in parallel allow more current to flow than a single resistor. One way to visualise this is to think of a bucket of water with a hole in its base – water will leak out of the hole. What would happen if instead of one hole, the bucket now has two holes of the same size? More water would leak out of the bucket!

When resistors are in parallel, the combined resistance in parallel is calculated using the following equation:

Therefore, the resistance of a circuit with two 5 Ω resistors in parallel is calculated as:

To find R we must turn 1/R over:

And we can check this by applying Ohm’s law R = V/I

Task 3 – nichrome wires and resistance explained

In this task, you observed how the resistance of three different wires changed as a function of length and then plotted your measurements on a graph and discussed your findings with your classmates.

You should have noticed the following:

• Resistance is proportional to the length of the wire
• Wires with a larger cross-sectional area have a lower resistance.

And these observations are captured by the following equation which is used to calculate the resistance of a wire:

Where the symbol ρ (the Greek letter rho) is a constant that depends on the material the wire is made from (also called the resistivity of the material), l is the length and A the cross-sectional area.

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