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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

Instructor:
*Scott van Tonningen*

Scott has a Ph.D. in electrical engineering and has taught a variety of college-level engineering, math and science courses.

All electrical circuits have resistance, and the basic unit of resistance is the ohm. This lesson provides a deeper understanding of the ohm, how to calculate resistance in ohms, and a quiz to test your understanding.

Next time you have water in the bathtub (make sure it's full), start draining it and see how many seconds it takes for the level to drop down exactly one inch. Stop the drain, refill the tub and cover half the drain. Time it again. It should take twice as long for the water level to go down one inch.

Here's what happened. The force of the water is essentially constant during this experiment and is due to the weight of the water pressing on the drain. When you cover half the drain, you're doubling the resistance that the drain presents to the water. This cuts the flow rate of water through the drain in half. Halving the flow rate doubles the amount of time it takes to drain.

This is precisely what happens with electrical charge in a circuit. An electrical source provides a constant force (voltage) just like the weight of the water. The flow of electrical charge through the circuit (current) is like the flow rate of the water. The wires or devices in the circuit are like the drain, providing a certain amount of resistance. The quantities and units we will discuss are shown on the following table, with International System (SI) derived units shown as well as electrical symbols:

Let's find out more about the ohm and how it works in electrical circuits.

An **ohm** is a unit of electrical resistance seen between two points across a resistor, conductor, device or circuit. One ohm means that a potential difference (voltage) of 1V between these two points produces a current of 1A. The following diagrams depict examples of how this might occur:

In general, this relationship between any voltage, current, and resistance is modeled by **Ohm's Law**, which we will define as an equation in the following form:

Suppose an unknown 'black box' has two electrical terminals. You connect a 6V battery and an ammeter (which measures current) in series with the black box as shown. Assume that the ammeter and the wires have zero resistance. A current of 60 mA (milliamps or thousandths of an amp) is measured in the circuit. What is the resistance, in ohms, of the black box?

We apply Ohm's Law to find:

Engineers and scientists are not usually known to be particularly humorous, but there are a few 'ohm jokes' out there worth sharing. See if you can figure out the well-known expressions portrayed by the following pictures (A, B and C):

Give up? A is 'Ohm on the Range;' B is 'Ohm free;' C is 'The ohm stretch.' Told you it was really bad humor! Okay, let's get back to the lesson.

Electrical power (wattage) is the product of voltage and current, so we can substitute Ohm's Law into the power equation and come up with a relationship for resistance based on power (in watts, W) and either voltage or current:

For example, if we know that a 75W light bulb is drawing 5 amps of current, we can find the internal resistance of the bulb:

Resistance is purposefully designed into resistors and integrated circuits using the resistivity of the material. **Resistivity** is defined as the degree to which a material resists the movement of electrons, as a function of volume. It is measured in terms of ohms per meter of length of the material, per meter squared of cross-sectional area of the material. This reduces simply to units of ohm-meters. The formula for resistance in terms of resistivity is:

Following is an example of a block of silicon with resistivity of 20 ohm-meters. We want to find the resistance, in ohms, measured from one side of the block to the other.

The resistance would be found as follows:

Let's try one more. What do you think this is?

Yep, it's the song, 'My Old Kentucky Ohm.'

The **ohm** is a unit of electrical resistance defined between two points in a circuit, or across a conductor, resistor or device. One ohm means a voltage of one volt between the two points creates a current of one amp. The mathematical relationship between resistance, voltage and current is given by **Ohm's Law**, which states that resistance (in ohms) is equal to voltage divided by current.

Electrical resistance impedes the flow of current much like a drain impedes the flow of water. The more restrictive the drain, the slower the water flows given a constant force. The same is true in electrical circuits - the higher the resistance, the smaller the current for a given electromotive force (voltage).

Resistance can be related to electrical power through a couple of additional formulas. The first states that resistance is equal to voltage squared divided by power. The second states that resistance is also power divided by current squared.

Resistance can also be found using the **resistivity** of a material. Resistivity is the degree to which the material resists the flow of electrons, as a function of volume. Resistance (in ohms) is equal to the resistivity (in ohm-m) times the length of material divided by its cross-sectional area.

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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