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.
