Question

Derive the formula R=rho l/a
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Answer 1

Answer:Derivation

Explanation:

R∝l ....eq.1

R∝1/A...eq.2

From 1&2

R∝l/A

Rho is a specific resistivity  constant

Therefore,

R=rho l/A

Answer 2

✳ To Derive:

$\large{ \circ\: \:{ \rm{ R = \rho \: \dfrac{L}{A} }}}$

✳ How to derive?

Depending upon the factors on which the resistance depends upon, we will combine them, and add the constant of proportionality to get the above equation.

✳ Derivation:

Resistance depends upon:

✒ Length of Conductor: The resistance of a given conductor is directly proportional to its length.

• $\large{ \rm{R \: \propto \: \: L......(1)}}$

✒ Area of cross section of a conductor: The resistance of a given conductor is inversely proportional to its area of cross section.

• $\large{ \rm{R \: \propto \: \dfrac{1}{A}.......(2)}}$

Mathematically, from (i) and (ii)

$\large{ \rm{ \longrightarrow \: R \: \propto \: \frac{L}{A} }} \\ \\ \rm{ \dag \: { \green{ \underline{replacing \: with \: constant \: of \: propotionality}}}} \\ \\ \large{ \rm{ \longrightarrow \: \boxed{ \red{ \rm{R= \rho \: \frac{L}{A} }}}}}$

Where, ρ is a constant of proportionality known as resistivity of the material of conductor. Resistivity is also known as Specific resistance.

$\large{ \therefore{ \underline{ \underline{ \purple{ \rm{Hence \: derived \: \dag}}}}}}$

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