Question

Verify the statement

${\mathcal{\color{purple}{R={\rho}\dfrac{A}{l}}}}$​

Answer 1

Answer :-

We have to verify the given statement that is,

$\frac{R \: \propto \rho \: l}{A}$

1) Take wire AB and now replace that wire with another same material and thickness but of double it's length .

• Now, Measure it's resistance by measuring V and I.

• Then we found that the resistance of wire doubled with that of wire AB

• So, we can conclude that,

Resistance of a conductor is directly proportional to its length.

2) Now, Replace the wire AB with another wire of the same material and same length but half of its cross sectional area.

• We can measure the redistance of wire by using relation R = V/I is twice the resistance of wire AB.

• So we can conclude that,

Resistance increases with the decrease in cross sectional area ie,

Resistance is inversely proportional to cross sectional area.

3) Now, Replace AB with a wire of same length and Same cross sectional area but of the some other material.

• Then we will found that the resistance of wire is different from that of wire AB.

• So we can say that,

The resistance of a conductor depends upon the nature of its material.

From the above observation we can conclude that,

1) R ∝ l. eq( 1 )

2) R ∝ 1/A eq( 2)

3) R ∝ ρ eq( 3)

From eq( 1 ) , ( 2 ) and ( 3) we get,

R = ρ * l / A

Where $\rho$ is a constant of proportionality and is called the specific resistance or resistivity. it depends on the nature of material.

Answer 2

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