# Ohm's Law and Voltage vs. Current Graphs

## Voltage vs. Current Graph

There are multiple units of measurement that are used to describe an electrical system. For instance, **current** and **voltage** are two forms of measurement used to describe properties of electricity that are often confused with one another. Current can be described as the flow of charges. For instance, if electricity were a falling ball, current would be the speed at which the ball passes a determined point between its drop and land point. Voltage is often compared to force. Using the same analogy, voltage would be the gravity that is pulling the ball towards the ground. These differences are summarized in the following table:

Type of Liquid | Voltage | Current |
---|---|---|

Definition | Force or pressure pushing electricity through a circuit | Rate at which electricity passes through a point in a circuit |

If a ball was dropped... | Voltage is the gravity pulling the ball towards the ground | Current is the speed at which a ball is falling at a given point |

Units | Volts (V) | Amps (A) |

Equation | V=IR | I=V/R |

Voltage, current, and **resistance** are all related. Resistance (measured in Ohms) prevents current from being able to flow. If a ball were dropped into water, it would not reach the floor as quickly as if it were dropped in air because the water creates resistance. The relationship between resistance (R), current (I), and voltage (V) can be described mathematically:

{eq}V=IR {/eq}

In this equation, voltage is also referred to as the **potential difference**, which is the difference in energy occurring at two different points along a circuit. Voltage and current can be graphed on a **voltage vs. current graph**, which depicts voltage on the x-axis and current on the y-axis. A voltage vs. current graph may be portrayed as a **current vs. potential difference graph**. In this instance, the x-axis represents the current and the y-axis represents the current.

### Voltage, Current, and Resistance Example

Michael is calculating the resistance in his circuit. Using the proper equipment, he measures the amplitude and voltage of the system. Michael finds that his circuit has a voltage of 0.4V and a current of 0.7A. Knowing that the material he uses supports a linear relationship between voltage and current, he calculates the following resistance:

{eq}V=IR {/eq}

{eq}0.4=0.7*R {/eq}

{eq}\frac{0.4}{0.7}=R {/eq}

{eq}R=0.57 {/eq}

Using the provided equation, Michael finds that his circuit has a resistance of 0.57 Ohms.

### Slope of Voltage vs. Current Graph

The slope of a voltage vs. current graph provides important information about a circuit. When the slope of the line is equal to 1, then the current and voltage increase proportionally. In some instances, the line may be a horizontal or vertical line. If the line is horizontal, then the current remains the same regardless of the change in voltage. Instead, voltage and resistance change. If the line is vertical, then even when the voltage is not changing, resistance and current are.

The slope of a graph is equal to the change in its rise over the change in its run. Because resistance is equal to the voltage divided by the current, the slope of a voltage vs. current graph is the inverse of the resistance. In a current vs. potential difference graph, the slope is equal to the resistance.

## Ohm's Law

The equation provided above reflects **Ohm's Law**, a mathematical relationship between current, voltage, and resistance first described by Georg Simon Ohm. Ohm's law can be rearranged as needed to solve for any of the 3 included variables. This equation is particularly helpful for determining resistance. Both voltage and current can be easily measured with a voltmeter and ammeter respectively. Because the relationship between these variables is relatively simple to compute, people today often use a **multimeter**, which measures current and voltage and calculates resistance at the same time.

### Ohm's Law Graph

Ohm's Law graphs can resemble the voltage vs. current graphs mentioned above and are used to depict changes in resistance. If resistance remains constant, the Ohm's graph will appear as a voltage vs. current graph with a slope of 1, meaning that voltage and current are increasing proportionately. However, the slope of an Ohm's Law graph may change depending on the type of material used within a circuit.

## Ohmic vs. Non-Ohmic Materials

When the slope of an Ohm's Law graph (and subsequently the resistance of a circuit) remains consistent, the circuit is composed of **Ohmic material**. Ohmic materials adhere to the equation provided in Ohm's Law and include materials such as metals, wires, and resistors. When the resistance of a circuit does not remain the same, the conducting material is **non-Ohmic**. This includes materials such as electrolytes, diodes, and filament lamps. Each non-Ohmic material can produce a unique Ohm's Law graph.

Ohmic materials are not always Ohmic in nature. For instance, a metal exposed to incredibly high temperatures will produce resistance slopes that are non-Ohmic in nature. While changing the temperature does not result in a non-Ohmic material becoming an Ohmic material, it may alter its relationship between voltage and current.

## Lesson Summary

**Current** is the flow rate of charges through a circuit while **voltage** is the force pushing charges through a circuit. They are related through **Ohm's Law**, which states that voltage is equal to the current multiplied by the **resistance**. Resistance prevents current from flowing throughout a circuit. On a **voltage vs. current graph**, voltage is depicted on the x-axis in volts and current on the y-axis in amps. The inverse of the slope is equal to the resistance. **Potential difference** is the amount of voltage that differs between two spots in a circuit. On a **current vs. potential difference graph**, potential difference is displayed on the y-axis in volts and current on the x-axis in amps. The slope of the line is equal to the resistance. Voltage, current, and resistance can be measured with a **multimeter**.

**Ohmic materials** are those that follow Ohm's law and maintain a linear relationship between voltage and current. When heated, Ohmic materials may act like **non-Ohmic materials**. Non-Ohmic materials are those that do not maintain a linear relationship between voltage and current and may have a curved line on a voltage vs. current graph.

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#### What does the slope of the current vs. voltage graph give?

The slope of the voltage vs. current graph is equivalent to the inverse of the resistance. The slope of the current vs. potential difference graph is equal to the resistance.

#### What is the relationship between voltage and current?

Current, voltage, and resistance are related through Ohm's Law. Voltage is equal to the resistance of a circuit multiplied by its current.

#### What is the relationship between current and voltage graphs?

Voltage and current may be depicted on voltage vs. current graphs, where voltage is on the x-axis and current is on the y-axis. Voltage may be reflected on the y-axis as potential difference in current vs. potential difference graphs.

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