Question

write the formula for the following: i) resistance in terms of length , area and resistivity ii) current in terms of resistance and voltage

Answer 1

Answer:

Resistivity or electric resistivity is certainly the inverse of the electrical conductivity. Resistivity is a fundamental property of a material and it demonstrates how strongly the material resists or conducts electric current. A low resistivity is a clear indication of a material which readily allows electric current. Moreover, the common representation of resistivity is by the Greek letter ρρ. Also, the SI unit of electrical resistivity happens to be the ohm-meter (ρρ-m).

Resistivity is certainly the measure of how strongly a particular material opposes the flow of electric current on conductors or resistors with a certain uniform cross-section. Furthermore, uniform cross-section is the one where the current flows in a uniform manner. Conductivity happens to be the reciprocal quantity which is a measure of the easiness by which a material permits the flow of current.

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Resistivity Formula

The resistivity formula can be represented as follows:

Resistivity = 1conductivity1conductivity

The equation can be represented as :

ρρ = 1σ1σ

Here:

σσ = conductivity

ρρ = resistivity

Furthermore, another formula for resistivity can be

ρρ = RALRAL

Here,

ρρ = resistance

R = resistance

A = cross-sectional

L = length

Resistivity Formula Derivation

The resistance R is definitely directly proportional to the length of the conductor. What this reflects is that resistance increases with an increase in the conductor’s length.

So, resistance (R) ∝∝ l (1)

The resistance R is certainly inversely proportional to the area of cross-section of a particular conductor. What this means is that R will decrease with an increase in the area of conductor and vice-versa. More area of the conductor leads to an efficient flow of electric current through more area and consequently decreases the resistance.

Therefore, resistance ∝∝ 1A1A of cross section of the conductor (A)

Or, R ∝∝ 1A1A (2)

Now from equation (1) and (2)

R ∝∝ lAlA

Or, R = plAplA (3)

Here ρρ (rho) happens to be the proportionality constant. Most noteworthy, it is the electrical resistivity of the material of conductors.

Now from equation (3)

RA = ρρl

Or its alternate can be, ρρ = RAlRAl

Solved Examples on Resistivity Formula

Q1 Find out the resistivity of the metal wire of 2 m length and 0.6 mm in the diameter if its resistance happens to be 50 Ω

A1 The given information contains:

Resistance (R) = 50 Ω

Length (l) = 2 m

Diameter = 0.6 mm

Therefore, the radius would be 0.3 mm = 3 × 10-4m

Resistivity (ρρ) = ?

The area of the cross section of wire is = πr2πr2

Or it can be A = 3.14 × (3×10-4)2

Also, A = 28.26 × 10-8 m2 = 2.826 × 10-9 m2

It is already known that

ρρ = RAlRAl

Or, ρρ = 50Ω×2.826×10−9m22m50Ω×2.826×10−9m22m

ρρ = 25 × 2.826 × 10-9Ωm

= 70.65 × 10-9Ωm

Finally, ρρ = 7.065 × 10-8Ωm

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Answer 2

1. R= rho length/area

2. I= V/R

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