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प्रश्न
A uniform wire of resistance 100 Ω is melted and recast as a wire whose length is double that of the original. What would be the resistance of the wire?
उत्तर
Let
Resistivity of the wire = ρ
Original length of the wire = l
New length of the wire = l'
Original area of the wire = A
New area of the wire = A'
Original resistance of the wire = R = 100 Ω
New resistance of the wire = R'
Given:-
l' = 2l
The volume of the wire remains constant. So,
\[Al = A'l'\]
\[ \Rightarrow A' = \frac{A}{2}\]
We know:-
\[R = \frac{\rho l}{A}\]
\[ \Rightarrow R' = \frac{\rho l'}{A'}\]
\[ \Rightarrow \frac{R'}{R} = \frac{l'A}{lA'}\]
\[ \because l' = 2l, A' = \frac{A}{2}\]
\[ \Rightarrow \frac{R'}{R} = \frac{\left( 2l \right)A}{l\left( \frac{A}{2} \right)} = 4\]
\[ \Rightarrow R' = 4R = 400 \Omega\]
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