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.

Pojęcia kluczowe

Term (symbol)	Meaning
Current ( $I$ ‍)	Measure of how much charge passes through a given area over time. SI units of $Ampere (A)$ ‍.
Ampere ( $A$ ‍)	Current equivalent to transferring $1 coulomb$ ‍ of charge per second. SI units of $\frac{C}{s}$ ‍.
Direct current (DC)	Constant flow of charge in one direction.
Resistor	Device used to reduce current flow.
Resistance ( $R$ ‍)	Measure of how much an object resists current flow. Depends on material, length, and cross sectional area. SI units of Ohms ( $Ω$ ‍).
Resistivity ( $ρ$ ‍)	Measure of how much a specific material resists current flow. SI units of $Ω \cdot m$ ‍.
Ohm ( $Ω$ ‍)	The unit of electrical resistance. SI units of $\frac{kg \cdot m^{2}}{s^{3} \cdot A^{2}}$ ‍.

Równania

Equation	Symbols	Meaning in words
$I = \frac{Δ q}{Δ t}$ ‍	$I$ ‍ is current, $Δ q$ ‍ is net charge, and $Δ t$ ‍ is change in time.	Current is the change in charge over the change in time.
$R = \frac{ρ l}{A}$ ‍	$R$ ‍ is resistance, $ρ$ ‍ is resistivity, $l$ ‍ is length, and $A$ ‍ is cross sectional area	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 electron current, and its direction is opposite to

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.

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

ρ

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

Dowiedz się więcej

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

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