The increased resistance of a wire if its length is doubled and original cross sectional area is halved will be: (Given R = original resistance of wire)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 4R \)
The resistance of a wire is proportional to its length and inversely proportional to its area of cross-section; the resistivity \( \rho \) of the material does not change.
\( \displaystyle R = \frac{\rho l}{A} \)
Putting \( l' = 2l \) and \( A' = A/2 \):
\( \displaystyle R' = \frac{\rho\,(2l)}{A/2} = 4\,\frac{\rho l}{A} = 4R \)
The new (increased) resistance is \( 4R \).