## Ohm’s Law

5.4 Ohm’s Law

### Learning Objectives

By the end of this section, you will be able to:

- Describe Ohm’s law
- Recognize when Ohm’s law applies and when it does not

### Ohm’s Law

The current in a wire is proportional to the potential difference that drives it: . But what keeps the current steady is a frictional force that opposes the motion of the charges. This frictional force gives rise to a property of the wire called **Resistance**. The more resistance a wire has, the more it will try to slow down the current. So the current is inversely proportional to the resistance: (as R gets bigger, I gets smaller). We can put these two expressions together to get what is known as Ohm’s Law:

If you applied a potential difference across a wire and then measured the current, the current would increase proportionally with the potential difference:

Here we’ve plotted the current on the y-axis because it is the dependent variable – it depends on the voltage that is applied. The slope of this line is 1/R, where R is the resistance of the wire.

All materials will have some amount of resistance (except for special materials called superconductors, but we won’t have time to talk about those in this course, sorry). The units for resistance are derived from V/A and are called Ohms, symbol: Ω (the Greek letter Omega), We even have devices that are manufactured to have a specific amount of resistance and these devices are called **resistors**. This is a picture of some resistors that are used in electric circuits to reduce the current in a circuit by a specific amount:

### Analyzing Simple Circuits

In this video I show a simulation of electric current flowing in a circuit to light up a light bulb. After the video, you can play around with the simulation too.

Circuit Construction Kit simulation

In the following two videos, you can see how we make measurements in a circuit. We use a **voltmeter** to measure the potential difference between two points and we use an **ammeter** to measure the current at any point in the circuit.

Using the measurements I made in these videos, I want you to determine the resistance of the resistor.

### Putting it all together: current, resistance, and Ohm’s law

Pause & Predict 5.4.1 |
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What diameter will result in the same resistance? |

Pause & Predict 5.4.2 |
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What is the current through the resistor? |

**Practice!**

Practice 5.4.1 |
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A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the shape of a coil and used as a filament in an incandescent light bulb. When the light bulb is connected to a battery, a current of 0.526 A is measured through the filament. What is the resistance in this tungsten filament? (Tungsten has a resistivity of 4.9 x 10^{-8} Ω·m) |

Practice 5.4.2 |
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Light bulb A contains a coil filament made from a tungsten wire that is 580 mm long and has a 0.046-mm-diameter circular cross section. Light bulb B also has a coil filament made of tungsten, but it’s length is twice as long as the filament in light bulb A and it’s diameter is half that of light bulb A. What is the ratio of the resistance of light bulb B to the resistance of light bulb A? |

Practice 5.4.3 |
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A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the shape of a coil and used as a filament in an incandescent light bulb. When the light bulb is connected to a battery, a current of 0.526 A is measured through the filament. What is the voltage of the battery that would produce this current in the filament? (Tungsten has a resistivity of 4.9 x 10^{-8} Ω·m) |