Question

A wire of resistance \(5\,\Omega\) is drawn out so that its length is increased to twice its original length, its new resistance is:

• A. \(45\,\Omega\)
• B. \(54\,\Omega\)
• C. \(20\,\Omega\)
• D. \(5\,\Omega\)

Hint:

If length doubles \(\Rightarrow\) resistance becomes 4 times (volume constant).

Answer 1

The Correct Option is C

Concept: \[ R = \rho \frac{L}{A} \] When wire is stretched, volume remains constant: \[ LA = \text{constant} \]

Step 1: New dimensions.
\[ L' = 2L \Rightarrow A' = \frac{A}{2} \]

Step 2: New resistance.
\[ R' = \rho \frac{2L}{A/2} = \rho \frac{4L}{A} = 4R \] \[ R' = 4 \times 5 = 20\,\Omega \]