Question

A wire of resistance 10 \(\Omega\) is stretched to twice its original length. What is the new resistance?

• A. 200 \(\Omega\)
• B. 40 \(\Omega\)
• C. 50 \(\Omega\)
• D. 10 \(\Omega\)

Hint:

When a wire is stretched, its length increases and cross-sectional area decreases, leading to an increase in resistance by a factor of 4.

Answer 1

The Correct Option is B

The resistance \(R\) of a wire is given by the formula: \[ R = \rho \frac{L}{A} \] where \(\rho\) is the resistivity, \(L\) is the length, and \(A\) is the cross-sectional area. When the wire is stretched to twice its original length, the new resistance will be: \[ R_{\text{new}} = R_0 \times \left(\frac{L_{\text{new}}}{L_0}\right) \times \left(\frac{A_0}{A_{\text{new}}}\right) \] Since the length is doubled, the area decreases by a factor of 4 (because the volume remains constant). So, the resistance increases by a factor of 4: \[ R_{\text{new}} = 10 \times 4 = 40 \, \Omega \]
Final answer
Answer: \(\boxed{40 \, \Omega}\)