Question

A uniform metal wire carries a current of 2 A when an ideal cell of 3.4 V is connected across it. The wire has mass \( 8.92 \times 10^{-3} \, \text{kg} \), density \( 8.92 \times 10^3 \, \text{kg/m}^3 \) and resistivity \( 1.7 \times 10^{-8} \, \Omega \text{m} \). Then the length of the wire is

• A. 5 m
• B. 6.8 m
• C. 10 m
• D. 15.6 m

Hint:

To find the length of a wire given its resistivity, use the formula for resistance \( R = \rho \frac{L}{A} \) and solve for \( L \).

Answer 1

The Correct Option is C

The power dissipated in a resistor is given by: \[ P = I^2 R \] The resistance \( R \) of the wire is given by: \[ R = \rho \frac{L}{A} \] Where: - \( \rho = 1.7 \times 10^{-8} \, \Omega \text{m} \) is the resistivity, - \( A = \frac{m}{\rho} \) is the cross-sectional area of the wire, - \( L \) is the length of the wire. Using the provided values and applying the formula, the length \( L \) is determined to be 10 m. Thus, the length of the wire is \( \boxed{10 \, \text{m}} \).