\begin{gathered}We \: know \: that \: Resistance: \\ \\ R= \frac{ρ ℓ}{A} \end{gathered}
WeknowthatResistance:
R=
A
ρ ℓ
\begin{gathered}R= \frac{ρ ℓ}{A} \times \frac{ℓ}{ℓ} \\ \\ = \frac{p {ℓ}^{2} }{v} \\ \end{gathered}
R=
A
ρ ℓ
×
ℓ
ℓ
=
v
pℓ
2
\begin{gathered}Also, \: since \: the \: material \: is \\ \: same, \: therefore \: resistivity \\ \: ρ \\ is \: also \: constant.\end{gathered}
Also,sincethematerialis
same,thereforeresistivity
ρ
isalsoconstant.
R∝ℓ R∝ℓ
\begin{gathered} \frac{R_{1}}{R_{2}} = ( \frac{ℓ _{1} < /h2 > < h2 > }{ℓ_{2}} ) {}^{2} \\ \end{gathered}
R
2
R
1
=(
ℓ
2
ℓ
1
</h2><h2>
)
2
\begin{gathered}R_{2} = ( \frac{ℓ _{2} < /h2 > < h2 > }{ℓ_{1}} ) {}^{2} \\ \\ R_{1} = ( \frac{nℓ _{1}}{ℓ _{1}} ) {}^{2} \\ \\ R=Rn {}^{2} \end{gathered}
R
2
=(
ℓ
1
ℓ
2
</h2><h2>
)
2
R
1
=(
ℓ
1
nℓ
1
)
2
R=Rn
2