Question

Why resistance and resistivity not numerically equal.pls explain with the fact that resistivity is independent of size but resistance not.

Answer 1

Answer:

Resistance is the property by the virtue of which a conductor tries to prevent the movement of electrons and hence prevent current flow.

Whereas Resistivity is a materialistic property dependent solely on the type of material.

The relationship between resistance and resistivity is :

$\boxed{ \red{ \huge{R = \rho \: \bigg\{ \dfrac{length}{area} \bigg\}}}}$

From this equation, we can easily understand that Resistance and resistivity are not numerically equal in all cases. They will be equal only when length and area are 1 unit respectively.

From this equation, we can easily understand that Resistance depends on the size of the conductor , whereas Resistivity (ρ) being is materialistic property is not dependent on size.

Answer 2

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$</p><p>\tt{\purple{Why\: Resistance\:And\: Resistivity\:Are\:Not\:Numerically\:Equal \: - }}$

1. Resistance depends on Length.

Larger cross sections have less resistance, and longer conductors have more resistance.

1. Resistivity is a constant.

1. Dimension of resistance is Ohm in SI Units

1. Dimension of resistivity is Ohm / Metre in SI Units

$\tt{ \red{resistivity= \rho \times \frac{L}{A} }}$

L is the length of the conductor and A is the cross sectional area.

$\tt { \orange{ \rho = \: L \:only \: when \: \frac{L}{A} = unity.}}$