##
**Resistance and Resistivity**

Resistance and Resistivity |

The measure of opposition to flow of electric charge through a conductor due to continuous collisions with ionic cores (neighboring atoms) is called

**resistance 'R'**of a conductor is the ratio between the potential difference applied across the ends of the conductor to the amount of current passing through it, provided the physical conditions of the conductor (for example temperature) do not change. Thus

**Resistance**= R = V / I = Volts / Ampere

To answer the queries why electric current if starts to flow after the application of potential difference consider a conductor whose ends are maintained at a constant

**potential difference 'V'**.

An

**electric field (**

**will be developed inside the conductor as given by the relation**

**Ē**)**V**= E.d

**current I**. In electrostatic equilibrium, the

**electric field**must be zero inside the conductor but when a conductor carries a current, it is no longer in electrostatic equilibrium and free charges drift down the conductor driven by the applied electric field.

**SI unit of Resistance**is the ohm (Ω).

1 ohm = 1 volt / 1 ampere

R = V / I

When **one-volt potential difference**across a conductor causes

**the one-ampere current**through it, the resistance of the conductor will be one ohm.

**Ohm symbol**is Ω.

The

**reciprocal of resistance**is called

**conductance (G)**of the conductor such that

**G**= 1 / R ⟹

**G**= 1 / 1ohm

**G**= 1 / Ω ⟹

**G**= Ω⁻¹

**The resistivity**of a conductor is the resistance per unit length per unit area of the conductor. If a conductor has length

**'L'**and its cross-sectional area

**'A'**then the resistance of the conductor will depend on its

**length**and

**cross-sectional area**as given by the following relation.

**R**∝ L

**R**∝ 1 / A

OR

**R**∝ L / A

OR

**R**= ρL / A ➜ 1

**ρ**= R x A / L

**R**= V / I Coulumb's law

Putting this value in equation 1 we have

**ρ**= V / I x A / L ➜ 2

**ρ**= V / J.L ➜ 3

**V**= E.L

**E**= V / L

**ρ**= E / J

**resistivity and current density**.

**Editors Recommendations:**

Resistance and Resistivity
Reviewed by Abdullah
on
July 12, 2020
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