Video: Calculating Currents Using Ohm’s Law

A resistor of resistance 1.8 kΩ is connected across a battery of emf 5.0 V. What is the current through the resistor?

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Video Transcript

A resistor of resistance 1.8 kiloohms is connected across a battery of emf 5.0 volts. What is the current through the resistor?

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 ohms.

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 resistor.

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