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CLEP Natural Sciences: Study Guide & Test Prep25 chapters | 277 lessons

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Lesson Transcript

Instructor:
*Jim Heald*

Jim has taught undergraduate engineering courses and has a master's degree in mechanical engineering.

Did you know that electrical current is affected by the voltage and resistance in a circuit? In this lesson, we'll use Ohm's law, which tells us how current, voltage, and resistance are related, as we work through several electric circuit examples.

This past weekend, I was out in the garden watering the flowers when suddenly the flow of water nearly stopped. I looked behind me and realized there was a kink in the hose that was restricting the water flow. After I straightened out the kink, the water flow came back and I resumed my watering. But, a few minutes later, the water flow slowed down again. I looked for another kink in the hose, but this time I couldn't find one. I went in the house and found that my roommate was taking a shower while running the washing machine and the dishwasher all at the same time! Our water pump couldn't keep up with so much demand for water, and as a result, the water pressure to my garden hose had dropped, which reduced the water flow.

This got me thinking about how similar water flowing through a hose is to electric current in a circuit. Just like the water flow was determined by the amount of pressure and resistance in the hose, electric current is determined by the amount of voltage and resistance in an electric circuit.

The relationship between voltage, current, and resistance is described by **Ohm's law**. This equation, *i* = *v*/*r*, tells us that the current, *i*, flowing through a circuit is directly proportional to the voltage, *v*, and inversely proportional to the resistance, *r*. In other words, if we increase the voltage, then the current will increase. But, if we increase the resistance, then the current will decrease. We saw these concepts in action with the garden hose. Increasing the pressure caused the flow to increase, but getting a kink in the hose increased the resistance, which caused the flow to decrease.

The way the equation is written here, it would be easy to use Ohm's law to figure out the current if we know the voltage and the resistance. But, what if we wanted to solve for the voltage or the resistance instead? One way to do this would be to rearrange the terms of the equation to solve for the other parameters, but there's an easier way. The diagram above will give us the appropriate equation to solve for any unknown parameter without using any algebra. To use this diagram, we simply cover up the parameter we're trying to find to get the proper equation. This will make more sense once we start using it, so let's do some examples.

Below is a simple electric circuit that we'll use to do our examples. Our voltage source is a battery that is connected to a light bulb, which provides resistance to the electric current. To start off with, let's say our battery has a voltage of 10 volts, the light bulb has a resistance of 20 ohms, and we need to figure out the current flowing through the circuit. Using our diagram, we cover up the parameter that we're trying to find, which is current, or *i*, and that leaves us with the voltage, *v*, over the resistance, *r*. In other words, to find the current, we need to divide the voltage by the resistance. Doing the math, 10 volts divided by 20 ohms results in one half ampere of current flowing in the circuit.

Next, let's increase the voltage to see what happens to the current. We'll use the same light bulb but switch to a 20-volt battery. Using the same equation as before, we divide 20 volts by 20 ohms and we get 1 amp of current. As we can see, doubling the voltage caused the current to double as well. This makes sense when we think about the garden hose. If we increased the pressure in the hose, we would expect the flow of water to increase as well. It's always good to double-check your work by asking if the results match what you expected to happen.

If we increased the resistance of the light bulb, what would you expect to happen to the current? To find out, let's swap out our existing bulb with a different one that has a resistance of 40 ohms. Since we're still looking for the current, we use the same equation as before. Dividing 20 volts by 40 ohms gives us one half-ampere of current. This result tells us that doubling the resistance reduced the current by half. Is this what you expected? Thinking back to our hose, it makes sense that putting a kink in the hose would reduce the water flow, just like increasing the resistance in the circuit would reduce the current.

Thus far, we've only calculated the current in the circuit, but what if someone had swapped out our light bulb when we weren't looking and we needed to figure out the resistance of the new one? Well, we know the voltage of our battery is 20 volts, and we can measure the current in the circuit with a tool called an ammeter, so all that's left is to do some math. Using our diagram, we cover up the parameter that we're trying to find, which is the resistance, *r*. The diagram now shows us that we need to divide the voltage by the current. If our ammeter measured a current of 5 amperes flowing through the circuit, then the resistance is equal to 20 volts divided by 5 amperes, which is 4 ohms

Finally, imagine that someone replaced our battery and we needed to figure out its voltage. The process is pretty much the same. We know our new bulb has 4 ohms of resistance, and we can measure the current in the circuit with the ammeter. Using the diagram, we cover up the voltage, *v*, which tells us that we need to multiply the current by the resistance. If the ammeter measured a current of 3 amperes, then the voltage would be 3 amperes multiplied by 4 ohms, which is 12 volts. That's all there is to it. By knowing any two of the three parameters, we can always calculate the third by using Ohm's law.

Ohm's law defines the relationship between the voltage, current, and resistance in an electric circuit: *i* = *v*/*r*. The current is directly proportional to the voltage and inversely proportional to the resistance. This means that increasing the voltage will cause the current to increase, while increasing the resistance will cause the current to decrease. Knowing any two of the three parameters allows us to calculate the third, unknown parameter. We can do this by rearranging the terms in the Ohm's law equation or by using the diagram found above in the lesson. Covering up the parameter that we're trying to find shows us the appropriate equation using the two known parameters.

At the conclusion of this lesson, you will be able to:

- Describe the relationship between voltage, current, and resistance using Ohm's law
- Write the equation for Ohm's law
- Explain how you can find any one of the three variables in the equation for Ohm's law if you know the other two
- Calculate any of the three variables using the Ohm's law equation

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CLEP Natural Sciences: Study Guide & Test Prep25 chapters | 277 lessons

- Go to Mechanics

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