A resistor of resistance 1.8
kiloohms is connected across a battery of emf 5.0 volts. What is the current through the
If we sketch this resistor as part
of a circuit, we know it has a resistance 𝑅 of 1.8 kiloohms and that there is a
potential difference of 5.0 volts across this resistor. Knowing all that, we want to solve
for the current 𝐼 that runs through the resistor.
Ohm’s law tells us that the current
𝐼 when we multiply it by the value of the resistor 𝑅 is equal to the potential
difference across the resistor 𝑉.
Looking back at our circuit, we see
that the only place potential can drop is across the resistor. So therefore, that potential drop
𝑉 is equal simply to the potential supplied by the battery.
So then, rearranging Ohm’s law, we
can say that the current through this resistor is equal to the potential difference
across it divided by its resistance.
As we solve for this current, we
want to be careful plugging in our value for the resistance 𝑅. We make sure to include the fact
that it’s 1.8 kiloohms of resistance so that resistance is 1.8 times 10 to the third
Written in these units, we’re now
ready to divide this resistance in the 5.0 volts to solve for 𝐼.
𝐼 is 2.8 milliamps or 2.8
thousands of an amp. That’s the current through this