A 2300-ohm resistor in a circuit has a current of 100 milliamperes through it. What is the potential difference across the resistor?
In this exercise, we want to connect these three quantities of resistance, current, and potential difference. A great way to do this is through a relationship known as Ohm’s law. Ohm’s law says that for a constant resistance value that resistance multiplied by the current through the resistor is equal to the potential difference across it.
In our case, we’re told what those current and resistance values are. So it’s just a matter of substituting in for those and calculating the voltage. The one thing we want to be careful for is to consider the units in these values. Well, the value of the resistor is given in units of ohms, which is the base unit of resistance. The current we see is given in units of milliamperes, not amperes. This means if we were to substitute in these values and then multiply through as is, we will get an answer for potential difference in units of millivolts. But if we want an answer in volts and we do, then we’ll need to convert this value from milliamperes to amperes.
We know that 1000 milliamps is equal to one amp. And therefore, we can write 100 milliamperes as 100 times 10 to the negative third amps. And now, we see that the units when we multiply these two values together will be amps times ohms; that is, volts. Taking this product, we find it’s equal to 230 volts. That is the potential difference across the resistor.