Two wires, A and B, are made of the same material, but the length of A is 3 times that of B, and the cross-section of A is $$\frac{1}{4}$$​th of that of B. The resistance of A is:

Correct option is C

Correct Answer: (c) 12 times that of B

Explanation:
The resistance R of a wire is given by:

​$$R = \rho \frac{L}{A}$$​​

where:

• R = Resistance
• ρ = Resistivity (same for both wires, as the wires are made of the same material)
• L = Length of the wire
• A = Cross-sectional area of the wire

For wire A:

• L_A=3L_B​ (Length of A is 3 times that of B)
• ​$$A_A = \frac{1}{4}A_B​$$(Cross section of A is 1/4^th of that of B)
  

Resistance of A:

Resistance of B:

Ratio of resistances:

Thus, R_A=12R_B.

Information Booster:

·         Resistance is directly proportional to the length of the wire.

·         Resistance is inversely proportional to the cross-sectional area.

·         Materials with lower resistivity allow better electrical conductivity.

·         The formula $$R = \rho \frac{L}{A}$$​ is fundamental to analyzing resistance changes due to dimensions.

·         Altering both the length and cross-sectional area significantly impacts the resistance.