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Question Video: Determining the Resistance of a Bulb Connected to an Ammeter and a Voltmeter Science

The diagram shows an electric circuit consisting of a cell, a bulb, a voltmeter, and an ammeter. The readings of the ammeter and the voltmeter are shown on the diagram. What is the resistance of the bulb?

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Video Transcript

The diagram below shows an electric circuit consisting of a cell, a bulb, a voltmeter, and an ammeter. The readings of the ammeter and the voltmeter are shown in the diagram. What is the resistance of the bulb?

In order to find this value of resistance, we will need to look at what information is given to us in the diagram. The circuit contains a cell with an unmarked potential difference, a bulb, a voltmeter with a potential difference between the two points of one volt, and an ammeter, which reads a current of one ampere. So with this information, we can start determining the value of resistance of this bulb, which we can just call 𝑅.

It may seem concerning that we don’t have a value of potential difference for the energy cell. But we don’t really need to know it in order to find this bulb’s resistance. To see why, let’s recall a form of the equation that can relate resistance to the other variables present in this problem, Ohm’s law. Ohm’s law states that the value of resistance 𝑅 is equal to the potential difference 𝑉 divided by the current 𝐼.

So we can see that there may be a problem here. We can give the value of the potential difference read by the voltmeter, sure, but do we use that or the unknown value of the power cell? Well, when we use this equation to find the resistance of the bulb specifically, the value we need to use for the potential difference will only need to be the one for the potential difference across the bulb, not the general potential difference for the circuit provided by the cell. This means we don’t need to know the value for the cell at all. We just need the reading the voltmeter gives us.

So with these readings from the ammeter and voltmeter, we can find the resistance of the bulb. Looking back at the expression of Ohm’s law in terms of resistance, let’s set up our equation. The value of potential difference we have here is one volt, given from the reading of the voltmeter. The value of current we have is one ampere, given from the reading of the ammeter.

Regarding the units of this expression, the units of volts divided by the units of amperes will produce units of ohms. Ohms are expressed with the Greek letter Ω. So looking at our numbers, when we divide one volt by one ampere, we should get an answer of just one ohm. This means that the resistance of the bulb in this circuit using the values from the ammeter and voltmeter is one ohm.

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