Question

A coil of length \(l\) and area of cross-section \(A\) has resistance \(R\). If the length is increased to 3 times and area decreases to \(A/3\), then the new resistance is:

• A. \(9R\)
• B. \(3R\)
• C. \(R/3\)
• D. \(R/9\)

Hint:

Resistance is directly proportional to length and inversely proportional to the cross-sectional area. If the length increases by a factor of 3 and the area decreases by a factor of 3, the resistance increases by a factor of 9.

Answer 1

The Correct Option is A

The resistance of a conductor is given by the formula: \[ R = \rho \frac{l}{A} \] Where: - \(\rho\) is the resistivity of the material, - \(l\) is the length of the conductor, - \(A\) is the cross-sectional area. Now, if the length is increased by a factor of 3 and the area is decreased by a factor of 3, the new resistance \(R_{\text{new}}\) will be: \[ R_{\text{new}} = \rho \frac{3l}{A/3} = \rho \frac{9l}{A} = 9R \] Thus, the new resistance is 9 times the original resistance.