Question

If resistivity is \( 1.7 \times 10^{-6} \) \( \Omega \)cm, area of cross-section is \( 19.6 \times 10^{-8} \) m\(^2\), length is 31.4 m, the resistance is found to be

• A. 1.72 \( \Omega \)
• B. 2.72 \( \Omega \)
• C. 3.72 \( \Omega \)
• D. 4.72 \( \Omega \)

Hint:

The resistance of a wire depends on its resistivity, length, and cross-sectional area. Higher length increases resistance, while a larger area reduces it.

Answer 1

The Correct Option is B

The resistance (\( R \)) of a conductor is given by Ohm’s Law: \[ R = \rho \frac{L}{A} \] where: - \( \rho = 1.7 \times 10^{-6} \) \( \Omega \)cm = \( 1.7 \times 10^{-8} \) \( \Omega \)m (converted to SI units), - \( L = 31.4 \) m (length), - \( A = 19.6 \times 10^{-8} \) m\(^2\) (cross-sectional area).
Step 1: Substituting the Values \[ R = \frac{(1.7 \times 10^{-8}) \times (31.4)}{19.6 \times 10^{-8}} \]


Step 2: Simplifying the Expression \[ R = \frac{5.338 \times 10^{-7}}{19.6 \times 10^{-8}} \] \[ R = \frac{5.338}{1.96} \] \[ R \approx 2.72 \, \Omega \]


Step 3: Evaluating the Options - Option (A) - Incorrect: 1.72 \( \Omega \) is too low. - Option (B) - Correct: 2.72 \( \Omega \) matches our calculation. - Option (C) - Incorrect: 3.72 \( \Omega \) is too high. - Option (D) - Incorrect: 4.72 \( \Omega \) is incorrect.


Step 4: Conclusion Since the calculated resistance is 2.72 \( \Omega \), the correct answer is option (B).