A resistor in a circuit has a potential difference of 20 volts across it. The current through the resistor is 0.4 milliamps. What is the resistance of the resistor?
The first thing to do is to underline all of the important information that’s been given to us in the question. So we know we’ve got a resistor. And we know that it’s got a potential difference of 20 volts across it. We also know that the current through the resistor is 0.4 milliamps. What we’re being asked to do is to find the resistance of the resistor. We can write all of this information down in a separate column, by the way, in order to make it more succinct and easy to digest. And that’s exactly what we’ve done here. So we’ve labeled the 𝑝𝑑, or potential difference, as being 20 volts. The current is 0.4 milliamps. And we want to find out the resistance. Which means that we need to find a relationship that links together the potential difference, the current, and the resistance of a component in a circuit.
Ohm’s law is exactly this relationship. What it says is that 𝑉, the potential difference or voltage across a component, is equal to the current 𝐼 multiplied by its resistance 𝑅. It’s also worth noting the standard units that we use for each one of these quantities. Voltage, or potential difference, is usually given in volts. Current is in amps. And the resistance is in the units of ohms. So if we want to find out the resistance of the resistor in the standard unit of ohms, then we also need to have a voltage, or potential difference, in volts, which we already have, and a current in amps. But here, we’ve got it in milliamps.
So the first thing to do is to convert a current from milliamps to amps. The conversion is as follows: 0.4 milliamps is the same as 0.4 times 10 to the negative three amps. The reason for this is that one milli something is defined as one times 10 to the negative three multiplied by that something. So 0.4 milliamps is the same as 0.4 times 10 to the negative three amps. We can literally just think of it as replacing the “milli” in milliamps with times 10 to the negative three. This is quite a convenient way of thinking about it. And it actually works for other prefixes as well. For example, another prefix is kilo, shortened to 𝐾. kilo means 1000 or, in other words, 10 to the power of three. Therefore, a kilogram, which is a measure of mass, is the same as one times 10 to the power of three grams. And so 0.4 kilograms is the same as 0.4 times 10 to the three grams. We’re just replacing the “kilo” with 10 to the power of three, just like we replaced “milli” with 10 to the power of negative three.
So that’s a quick aside on prefixes and how we can substitute them in to give us the units that we want. But let’s get back to our question. So we’ve converted our current into amps, which is exactly how we need it. Which means, we could stop playing around with Ohm’s law in order to give us the resistance of the resistor. To find the resistance, we need to rearrange the equation so that we only have resistance on one side. We could do this by dividing both sides of the equation by the current. That leaves us with the voltage divided by the current is equal to the resistance.
So all that’s left is to plug in our values for the potential difference or voltage, 20 volts, and the current, 0.4 times 10 to the negative three amps. And that will give us the resistance. Once we evaluate the fraction, we get 50000. Which means that our final answer is: the resistance of the resistor is 50000 ohms.