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### Course: AP®︎/College Physics 1 > Unit 11

Lesson 1: Electric current, resistivity, and Ohm's law# Current, resistance, and resistivity review

Review the key terms, equations, and skills related to current, resistance, and resistivity, including how to find the current direction and what resistance depends on.

## Key terms

Term (symbol) | Meaning | |
---|---|---|

Current ( | Measure of how much charge passes through a given area over time. SI units of | |

Ampere ( | Current equivalent to transferring | |

Direct current (DC) | Constant flow of charge in one direction. | |

Resistor | Device used to reduce current flow. | |

Resistance ( | Measure of how much an object resists current flow. Depends on material, length, and cross sectional area. SI units of Ohms ( | |

Resistivity ( | Measure of how much a specific material resists current flow. SI units of | |

Ohm ( | The unit of electrical resistance. SI units of |

## Equations

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

Current is the change in charge over the change in time. | ||

Resistance is proportional to resistivity and length, and inversely proportional to cross sectional area. |

## How to visualize the current

Current measures the flow of charges through an area over time. Figure 1 shows a wire with charges $q$ moving to the left through the wire, which has a cross sectional area $A$ . Imagine we counted how many charges passed through the cross sectional area in one second. This rate is the current.

## Finding the current direction

Current direction is designated by the symbol $I$ along with an arrow and always refers to the flow of positive charge as shown in Figure 2A. This is sometimes called

**conventional current**.In conductors such as wires, the electrons are the only charge that move. The electrons flow opposite to $I$ (see Figure 2A). The direction of the flow of electrons is called $I$ (see Figure 2B). The convention of $I$ representing the flow of positive charge is a historical convention that is equivalent to negative charge flowing in the opposite direction.

**electron current**, and its direction is opposite to## What does resistance depend on?

Resistance depends on an object’s size, shape, and material. In Figure 3 below, the cylinder's resistance is directly proportional to its length $l$ . The longer the cylinder, the higher the resistance.

Additionally, the resistance is inversely proportional to the cross sectional area $A$ . If the diameter of the cylinder is doubled, the cross-sectional area increases by a factor of $4$ . Therefore, resistance decreases by a factor of $4$ .

The resistivity $\rho $ of a material depends on the molecular and atomic structure, and is temperature-dependent. For most conductors, resistivity increases with increasing temperature.

## Learn more

For deeper explanations of current and resistance, see our video on resistivity and conductivity.

## Want to join the conversation?

- Can there be a resistance in a vacuum even if the liquid hits that walls or other objects within the vacuum?(6 votes)
- It's important to remember that water through a tube is only an analogy. A tool to help describe physical interactions. Our senses were not designed to observe "subatomic particle-wave electron thingys" but by connecting them to real life phenom we're familiar with we can better learn about the universe... Hopefully you keep that in mind. In terms of your question, yes, if there is a pressure difference and a tube connecting the ends, water will flow; if your tube is filled of stone there will be more "resistance".(17 votes)

- If the electrons are the ones who move in a current,then wouldn't the atoms become unstable? I mean as we know that the electrons move in orbital shells around the positively charged atomic nucleus then how are they able to seperate from the atom and move freely in a current....please help me to have a clearer image of this....( sorry if my question was found to be inappropriate but I just had to polish my basics).(4 votes)
- Only the valence electrons in a conductor metal atom usually are involved in the flow of current(1 to 3 out of the many electrons a metal atom has. Copper has 29). These valence electrons too are loosely bound to the nucleus and can be used for current flow easily, this is because on losing a certain amount of electrons these metal atoms actually gain stability in some ways.

Also even when they participate in current flow the electrons are still there near every metal atom(a bit like water flowing in a pipe).

So as a combination of all these factors it doesn't lead to unstability. But yes, if you tried to extract say 10, or even 5 electrons from Copper atom got them away then the copper atom would be quite unstable.

Feel free to ask a follow up!

Hope that helps!(6 votes)

- The electric current has magnitude as well as direction but its not a vector quantity,why?(4 votes)
- Current follows the direction of the wire it is placed in. If you bend the wire, the strength of the current does not change. The arrow is simply indicating the direction of positive charge.

So though current has magnitude, it's direction is not similar to that of a vectors 'direction'. If you connect a wire carrying 3A of current at a 90 degree angle with a wire carrying 4A, and allow the current to flow into a separate wire, the total current in the new wire will be 7A and not 5A (which you would have gotten if you added the current vectorially).(1 vote)

- Would the same principles and formulas apply for proticity as they do for electricity?(3 votes)
- If you're wondering whether the same principals apply to protons as with electrons, that's a definite no. If you mean "electricity, as in the flow of electrons, but positively charged" then essentially yes - but the positively-charged equivalent of an electron is the positron, which is an extremely rare particle in nature as we understand it. If we wanted to harness "positricity" the same way we do electricity, that would probably require the electric polarity of the entire universe be spontaneously flipped-- not a terribly likely occurrence.(1 vote)

- sorry about this question..

how can i rearrange the formula to get Length?

is L = RA/P??

thanks(4 votes)- yes. you multiply both sides of resistance formula R=ρL/A with A, and formula becomes RA=ρL, then you divide both sides with ρ, and formula becomes RA/ρ=L. same principle is valid for any kind of formulas rearrangements(1 vote)

- When using the current equation in order to find the current, how do you find the net charge?(2 votes)
- Either the amount of charge is given(might be an easy question then) or we might need to find it out with solving a few equations if data like voltages and resistance in a circuit are given(then by applying Ohm's law or those laws of Kirchhoff), or in some cases like in Chemistry where we might have to apply thermodynamic laws of Faraday in scenarios like electroplating and such.(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.(2 votes) - What if all the factors that affect resistance are increased by a particular value. How does one establish what happens to resistance itself then?(2 votes)
- If you calculate this out, you find that there is no change in resistance.

resistance = resistivity * length / area

factor*resisitivty * factor*length / factor*area

Since the cylider's cross-sectional area increases by the square of the factor, all the factors in the equation cancel out, leaving you with 1*the original equation, i.e. the original equation. So no resistance change.(1 vote)

- What is the use rheostat in verifying the Ohm's law through an electric circuit?

Question from the chapter Current Electricity from ICSE Board in India.(2 votes) - Why is the sigma lowercase?(1 vote)