This article is about the resistance formula and its derivation. Resistivity refers to the electrical resistance of a conductor of a given unit cross-sectional area and unit length. It’s definitely a feature of all materials. In addition, experts can use resistivity to compare different materials based on their ability to conduct electric current. High resistivity is the technical term for poor conductors.
Electrical resistivity is the resistance to electrical movement of a material from one end to the other. This is a simple and insightful metric for describing materials. This is the inverse of electrical conductivity. Resistivity Formula is represented by ρ and is proportional to both material resistance and volume. The cross-sectional area of a particular material is inversely proportional to its resistivity. Multiplying the resistance R of a test object, such as a wire, by its cross-sectional area A and dividing by its length l gives the resistivity. This is usually represented by the Greek letter rho. Ohm is the unit of resistance. The ratio of area in square metres to length in metres is simplified to metres in the meter-kilogram-second (mks) scheme. The unit of Resistivity Formula in the meter-kilogram-second system is the ohm-meter. If distance is measured in centimeters, resistivity can be expressed in ohm-centimeters. At 200°C (680°F), a very strong conductor such as hard copper has a resistivity of 1.77 x 10-8 ohm-meters or 1.77 x 10-6 ohm-centimeters. Electrical insulators, on the other hand, have a resistivity in the range of 1012 to 1012 ohms. Resistivity Formula values are often affected by material temperature. Resistance tables usually give values at 200 °C. The Resistivity Formula of metallic conductors increases with increasing temperature, while the resistivity of semiconductors such as carbon and silicon decreases with increasing temperature. Refer to Extramarks for more such learning materials.
What Is Resistivity?
Resistivity Formula or electrical resistivity is indeed the opposite of electrical conductivity. Resistivity is a fundamental property of materials that indicates the degree to which a material resists or conducts electric current. A low resistivity clearly indicates that the material is a good conductor of current. Furthermore, the usual expression for resistivity is the Greek letter ρ. The SI unit of electrical resistance is the ohmmeter (ρ-m).
Indeed, Resistivity Formula is a measure of how strongly a particular material resists current flow on a particular uniform cross-section conductor or resistor. A uniform cross-section is a cross-section through which the current flows uniformly. Conductivity is its reciprocal and is a measure of how easily a material conducts electrical current.
The resistance formula can be expressed as:
resistance = 1 conductivity
The formula can be expressed as:
σ = conductivity
ρ = resistivity
Additionally, another Resistivity Formula can be used.
ρ = RAL
ρ = resistance
R = resistance
A = cross section
L = length
Resistivity Formula Derivation
The resistance R is always directly proportional to the conductor length.This reflects the increase in resistance as the length of the conductor increases.
So resistance (R) ∝ l (1)
R is indeed inversely proportional to the cross-sectional area of a specific conductor. This means that R decreases with increasing conductor area and vice versa. A larger area conductor allows current to flow more efficiently over a larger area, thus reducing resistance. Therefore, the cross-sectional resistance of the conductor ∝ 1A (A)
or R ∝ 1A (2)
From equations (1) and (2)
or R = plA (3)
where ρ (rho) happens to be the constant of proportionality. Most notable is the electrical resistivity of the conductor material.
Now from equation (3)
RA = ρl
Or you can use ρ = RAl instead.
Solved Examples On Resistivity Formula
Q1 Find the Resistivity Formula for a metal wire with a length of 2m and a diameter of 0.6mm when the resistance happens to be 50Ω.
A1 Information provided includes:
Resistance (R) = 50Ω
Length (l) = 2m
Diameter = 0.6mm
So the radius is 0.3 mm = 3 × 10-4 m.
Resistance (ρ) = ?
The area of the wire cross section is = πr2
Or A = 3.14 × (3 × 10-4)2
Also, A = 28.26 × 10-8 m2 = 2.826 × 10-9 m2
We already know that
ρ = RAL
or ρ = 50Ω×2.826×10−9m22m
ρ = 25 × 2.826 × 10-9 Ωm
= 70.65 × 10-9 Ωm
Finally, ρ = 7.065 × 10-8 Ωm