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## High school physics

### Course: High school physics > Unit 12

Lesson 1: Electric current, resistivity, and Ohm's law# Electric potential difference and Ohm's law review

Review the key terms, equations, and skills related to Ohm's law, including how electric potential difference, current, and resistance are related.

## Key terms

Term | Meaning | |
---|---|---|

Battery | Device that transforms chemical energy into electrical energy. An ideal battery has no internal resistance. | |

Electric potential difference ( | Energy change per unit charge between two points. Also called voltage or electric potential. Has SI units of Volts | |

Electromotive force (EMF, | EMF is the potential difference produced by a source such as an ideal battery. Has SI units of |

## Equations

Equation | Symbols | Meaning in words |
---|---|---|

Current is directly proportional to electric potential difference and inversely proportional to resistance. |

## Ohm’s Law

Ohm’s law states that for some devices there is a relationship between electric potential difference, current, and resistance.

The equation is:
$I={\displaystyle \frac{\mathrm{\Delta}V}{R}}$

Where $I$ is current, $\mathrm{\Delta}V$ is electric potential difference, and $R$ is resistance.

### How are electric potential difference and current related?

For a given resistance $R$ , increasing the electric potential difference $\mathrm{\Delta}V$ increases the current $I$ and vice versa.

### How are current and resistance related?

For a given electric potential difference $\mathrm{\Delta}V$ , if the resistance $R$ increases, then the current $I$ decreases and vice versa.

### How are resistance and electric potential difference related?

For a given current $I$ , if the electric potential difference $\mathrm{\Delta}V$ increases, then the resistance $R$ also increases and vice versa.

## Analyzing electric potential difference across a resistor using Ohm’s law

If the current encounters resistance, the electric potential difference decreases according to Ohm’s law. We sometimes call this a voltage drop.

## Analyzing electric potential difference and current across a battery

A common source of electric potential is a battery, which is represented in diagrams by the symbol below (Figure 2). The short side is the negative end, with a lower electric potential, and the long side is the positive end, with a higher electric potential.

Electrons flow from the negative terminal to the positive terminal. Conventional current $I$ travels from the positive terminal (higher electric potential), through the circuit, and finally to the negative end (lower electric potential).

Current flow and electric potential difference can be better understood by using the analogy of a boulder rolling down a hill. At the top of the hill, the boulder has a lot of gravitational potential energy. Similarly, an electron has a lot of stored energy in the form of electric potential energy when it is at the negative terminal of a battery. The boulder will naturally fall toward the ground where potential energy is lower. The electron at the negative terminal of a battery will naturally flow toward the positive terminal, where the electric potential is lower.

As the boulder falls downward, the stored energy is converted to kinetic energy. As the electron flows across electrical components, the stored energy is converted into various forms of energy such as heat and light.

## Common mistakes and misconceptions

**Sometimes people think all devices follow Ohm’s law.**However, a device is only ohmic when the current is directly proportional to the electric potential difference, and inversely proportional to the resistance. If we plotted an electric potential vs. current graph for an ohmic device, the relationship would be linear (see Figure 3).

Some devices such as light bulbs are non-ohmic. This means that their electric potential difference-current graphs are non-linear, as in Figure 3. For non-ohmic devices, we can’t use $I={\displaystyle \frac{\mathrm{\Delta}V}{R}}$ to solve for an unknown.

## Learn more

For deeper explanations on electric potential and Ohm's law, see our video on circuits and Ohm's law.

To check your understanding and work toward mastering these concepts, check out the exercise on Ohm's law.

## Want to join the conversation?

- I was stuck in this place, where is says the electrons move to the positive terminal because the potential is lower.

" The boulder will naturally fall toward the ground where potential energy is lower. The electron at the negative terminal of a battery will naturally flow toward the positive terminal, where the electric potential is lower."

But a few paragraphs up it says the opposite..?

" The short side is the negative end, with a lower electric potential, and the long side is the positive end, with a higher electric potential."(19 votes)- The reason for this is that electrons are negatively charged. They are in a state of high potential when at the negative end and low potential at the positive end.

Before physicists knew that electrons moved, they assumed that positive charges were doing the moving. For this reason, conventional circuits state positive (+) to be high potential and negative (-) to be low potential.(14 votes)

- I couldn’t understand how non-ohmic devices work. How do non ohmic devices work if they do not follow a directly/indirect proportion to the electric potential difference and resistance?(6 votes)
- Resistance not only depends on length, area and type of the conductor, it also changes with temperature for some devices. So in a light bulb, because the temperature increases when it is illuminated, its resistance changes...we then have three variables and the relation between the current and the potential difference no longer gives a straight line (since its gradient, the resistance, is no longer a constant).

Devices whose temperature changes affect the resistance are called non-ohmic devices.(6 votes)

- I understand the equation for Ohms law and how electric potential is directly proportional to current and resistance. But conceptionally electric potential increasing when resistance increases doesn’t make sense. How does this relationship make sense conceptually? Wouldn’t voltage decrease if there is more resistance added?(5 votes)
- Electric potential would increase when resistance increases given a
**constant current**. Voltage would have to be higher to maintain the same current when resistance is higher.(5 votes)

- * "How are resistance and electric potential difference related?

For a given current III, if the electric potential difference \Delta VΔVdelta, V increases,*then the resistance R also increases*and vice versa." *

but u said in the video that R is constant?!(4 votes) - In the previous video, the speaker said that R is a constant and that with an increase in the V, there would only be a corresponding increase in I.

But here they state that "For a given current I, if the electric potential difference ΔV\Delta VΔVdelta, V increases, then the resistance R also increases and vice versa."(3 votes) - in the figure 3. The Current is plotted against x-axis and potential difference against y-axis isn't it wrong.(1 vote)
- Across a wire or lead, would there be a potential difference?(1 vote)
- A voltage is necessary for a current to flow. An electric current is the movement of charge (you can think of it as the movement of electrons, but that's a bit of a simplification). An electric field, which is a region with a voltage difference across it, causes the electrons to move.(1 vote)

- Can someone please explain why there is a "-" before ∆V in Figure 1 but a "+" before ∆V in Figure 2?(1 vote)
- The "-" represents negativity, and the "+" positivity. The ∆V represents the delta/change in voltage, and thus the signs tell us whether the change is positive or negative.(1 vote)

- As you mentioned, I assume this simple equation only holds for ohmic materials and only to the point of destruction.

As it is an abstraction, as soon as one takes temperature and other factors into account it will

become about semiconductors or nonlinearly behaving conductors - it is a simplified model but it suffices.(1 vote) - In the section:

How are resistance and electric potential difference related?

For a given current II, if the electric potential difference \Delta VΔV increases, then the resistance RR also increases and vice versa.

Should it not be like-"If the resistance R inc. then the potential diff. delV across the resistance also inc." Because, the resistance cannot be changed by inc or dec delV.(1 vote)