The resistance of a metal wire of length 1 m is 50 at 30 °C. Suppose the diameter of the wire is 0.3 mm. Now another wire has the same material and the same length (at 30 °C), but the diameter is increased to 0.6 mm. The resistance of the new wire is:

Correct option is A

The correct answer is (a) 12.5 Ω.

Explanation: Resistance and Cross-Sectional Area: Resistance is inversely proportional to the cross-sectional area of a wire. This means that if you double the diameter, the cross-sectional area increases by a factor of 4 (since area is proportional to the square of the diameter).

Calculation:

The resistance of the new wire is indeed 12.5 Ω.

• Relationship between Resistance and Cross-Sectional Area:
• Resistance (R) is inversely proportional to the cross-sectional area (A) of a conductor. This means that as the area increases, the resistance decreases.
• Mathematically, this can be represented as: R ∝ $$\frac{1}A$$​​
• Doubling the Diameter:
• If the diameter of a wire is doubled, its cross-sectional area increases by a factor of 4.
• This is because the area of a circle is proportional to the square of its diameter (A = πr²).
• Calculating New Resistance:
• Since the cross-sectional area quadruples, the resistance will decrease to one-fourth of its original value.
• Therefore, the new resistance (R2) is: $$R_2 = \frac{R_1}{4} = \frac{50 Ω}{4} = 12.5 Ω$$​​​​​​​​