# Ohm: Definition & Formula

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.

## The Bathtub Experiment

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.

## Definition of an Ohm

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:

## Ohm Example in a Simple Circuit

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.

## The Ohm and Wattage

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:

## Another Formula for the Ohm

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:

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