Question

The resistance of a wire is \(R\). It is bent at the middle by \(180^\circ\) and the ends are twisted together to make a shorter wire. The resistance of the new wire is:

• A. \(2R\)
• B. \(\dfrac{R}{2}\)
• C. \(\dfrac{R}{4}\)
• D. \(\dfrac{R}{8}\)

Hint:

When a wire is folded: \[ L \downarrow,\; A \uparrow \Rightarrow R \downarrow \] Track both changes carefully.

Answer 1

The Correct Option is C

Step 1: Length becomes half, area doubles.
Step 2: Resistance formula: \[ R=\rho\frac{L}{A} \]
Step 3: New resistance: \[ R'=\rho\frac{L/2}{2A}=\frac{R}{4} \]