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AP Physics 2: Exam Prep26 chapters | 141 lessons

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*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Crack open your computer, look at its motherboard, and you'll see tons of tiny resistors dotting its surface. In this lesson, you'll learn about these resistors and how you can calculate the resistance of a resistor and more.

Almost all electrical appliances and electronics make use of resistors. Open up your computer and look at the motherboard and you'll find all kinds of resistors dotting its surface. A **resistor** is a piece of material that impedes the electric current. Resistors are used to control both the voltage and the current running through a system. Without resistors, your electronics could easily burn out or overheat from too much electricity running through it. Resistors prevent that. So, even though they are tiny, they serve a very useful purpose.

There are many different resistors that an engineer can choose from. They are all rated by the amount of resistance each has. The bands on the resistor tell how much resistance it has.

Because the resistance of a resistor depends on the material it is made out of, the formula to calculate the resistance takes that into consideration.

The *R* stands for resistance. The Greek letter that looks like the letter *p* stands for the resistivity of the material used for the resistor. The *L* stands for the length of the resistor. And the *A* stands for the area of a cross section of the resistor. Resistance is measured in Ohms.

It is possible to have two same-sized resistors made of different materials with different resistances. But don't think it's just resistors that have resistance. The wires that conduct electricity themselves also have a certain amount of resistance. Anything that conducts electricity has a certain amount of resistance. Wires typically have much less resistance than a resistor that's made for the purpose of resisting electricity. You can have resistances of just of a few Ohms all the way up to millions of Ohms.

Here's an example of calculating the resistance of a carbon resistor that measures 0.005 meters (5 millimeters) long with a diameter of 0.001 meters (1 millimeter). This particular carbon resistor has a resistivity of 45 x 10-5 ohm-meter.

This carbon resistor has a resistance of approximately 2.86 Ohms. Notice that the symbol for Ohms is the big Greek letter omega.

All circuits that conduct electricity will follow what is called Ohm's Law. This law tells you how your voltage and current are related to your resistance.

The *R* stands for resistance, the *V* stands for voltage and the *I* stands for current. Your units are Ohms for resistance, Volts for voltage, and Amps for current. This formula tells you that your resistance is always equal to your voltage divided by the current. You can also say that your voltage is equal to your current multiplied by your resistance.

So, if your resistor in your circuit has a resistance of 100 Ohms and the current flowing through the circuit is 0.5 Amps, then the voltage of your circuit is calculated to be this:

Your circuit has a voltage of 50 Volts.

The way you place your resistors can change your resistance value differently as well.

If your resistors are placed in a series so they are connected with each other like in a necklace, then the total or equivalent resistance is the sum of your resistor values.

The current going through each resistor will be the same, but the voltage going through each resistor is different.

For example, say you have a 200 Ohm, 50 Ohm, and 25 Ohm resistor placed in series. Your total resistance of your circuit is 200 + 50 + 25 = 275 Ohms.

If your resistors are placed in parallel, meaning each resistor is connected to the same voltage source, then the equivalent resistance is found by using this formula.

The voltage for each resistor will be the same, but the current going through each resistor will be different.

For example, say you have the same 200 Ohm, 50 Ohm, and 25 Ohm resistors in parallel now. The total resistance can be found by doing this.

- 1/200 + 1/50 + 1/25 = 1/200 + 4/200 + 8/200 = 13/200 = 1/15.38

Notice how the last step divides both the numerator and denominator by the numerator. This gives you your 1 over the total resistance. Once you've done this, your total resistance is found to be 15.38 Ohms.

Let's review.

A **resistor** is a piece of material that impedes the electric current.

The resistance of a resistor is calculated by using this formula.

The *R* stands for resistance. The Greek letter that looks like the letter p stands for the resistivity of the material used for the resistor. The *L* stands for the length of the resistor. And the *A* stands for the area of a cross section of the resistor. Resistance is measured in Ohms and your Length and Area are measured in meters.

All circuits follow Ohm's Law that tells you the voltage of a circuit is equal to the current multiplied by the resistance.

The *R* stands for resistance. The *V* stands for voltage. And the *I* stands for current. Your units are Ohms for resistance, Volts for voltage, and Amps for current.

If your resistors are placed in series, then the equivalent resistance that is seen by the circuit is the sum of your resistor values.

On the other hand, if your resistors are placed in series, then your equivalent resistance is found by adding the inverses of your resistor values.

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AP Physics 2: Exam Prep26 chapters | 141 lessons

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