The radius of a wire having resistance R is made half and its length reduced to one - fourth of its original length. The new resistance of the wire will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → R
The resistance of a wire is \( R = \rho L/A \) with \( A = \pi r^{2} \), and the material (\( \rho \)) is unchanged.
\( r' = r/2 \;\Rightarrow\; A' = A/4 \)
\( L' = L/4 \)
\( \displaystyle R' = \frac{\rho L'}{A'} = \frac{\rho (L/4)}{(A/4)} = \frac{\rho L}{A} = R \)
The reduction of length and of area by the same factor leaves the resistance unchanged.