Power, Current & Potential Difference Across a Resistor

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

The current through a resistor depends on the potential difference across the resistor and the resistance. Ohm's law describes this relationship, and we'll learn how to determine the relationships between power, current, and voltage.

Voltage, Current, and Resistance

Every day, I take the same highway home from work. There are always a lot of cars, but there are multiple lanes so all the cars can usually travel about 60 miles per hour. One day, I got on the highway and the traffic was moving really slowly! Instead of going 60 mph, everyone was only moving about 30 mph. Looking at the road ahead, I could see that there was an accident that was blocking half of the lanes. Since the same number of cars were still on the highway, it was taking a lot longer for all those cars to get through this narrow section of the highway, causing the traffic to slow down.

A very similar thing happens in an electric circuit. In a circuit, tiny charged particles called electrons are moving through the wires of the circuit, just like the cars are moving on the highway. The rate at which these charges flow is called current.

The charges are able to move because they have been given some energy by the battery, which is a source of potential difference, also known as voltage.

Just like the accident on the highway slowed down the flow of cars, a resistor in an electric circuit slows down the flow of charge, reducing the current in the circuit. Resistors do more than just influence the amount of current in the circuit, though. Because it's difficult for the electrons to get through the resistor, they give up some energy as they pass through. That energy doesn't disappear: instead, it's transformed into other forms of energy, such as thermal energy and light. Light bulbs are one type of resistor that transform electrical energy into both thermal energy and light energy.

Light bulbs are resistors that transform electrical energy into light
voltage and current in a light bulb

Ohm's Law

If you wanted to experimentally determine the relationship between current, voltage, and resistance, what could you do?

A good way to determine this relationship would be to measure the current in a circuit composed of a voltage source, like a battery, and a resistor. You could change the amount of voltage, perhaps by varying the number of batteries used, and see how the current changed in response.

When measuring quantities like voltage, resistance, and current, it's really important to make sure that you are using the correct units. Typically, current is measured in units of Amperes (A), voltage is measured in Volts (V), and resistance is measured in Ohms.

Once you measured the current (in A) and voltage (in V), a graph could help you to understand the data. If you plotted the voltage on the y-axis and the current on the x-axis, you would get a graph similar to the one shown below:


This graph gives you some pretty important information about what is going on in the circuit. First, did you notice that the graph formed a straight line? This means that there is a direct relationship between current and voltage for this resistor. We call this relationship Ohm's law, which says that the current through a resistor is directly proportional to the voltage and inversely proportional to the resistance of the resistor.

Ohm's Law:

Current = Voltage/Resistance

I = V/R

This means that as voltage goes up, current does too. However, as the resistance goes up, the current goes down. Think back to the cars trying to get past the accident on the highway. The more lanes that are blocked by the accident, the slower the traffic will be able to move. Increasing the resistance of a resistor has the same effect on the current in the circuit.

The slope of the line on this graph is also important. Ohm's law can be rearranged and written as V = I x R. Since the current was plotted on the x-axis and the voltage was plotted on the y axis, the slope of this line is equal to the resistance of the resistor, so the resistance of this particular resistor must be 10 Ohms.

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