Two wires A and B are made of same material and have the same length but different cross-sectional areas. If the resistance of wire A is 9 times the resistance of wire B, the ratio of the radius of wire A to that of wire B is:

Correct option is D

The correct answer is (D) 1:3.

Explanation:

The resistance (R) of a wire is given by the formula:

$$R= \rho \frac{L}{A}$$​​

Where:

• ρ: Resistivity of the material (same for both wires as they are made of the same material)
• L: Length of the wire (same for both wires)
• A: Cross-sectional area of the wire (A=πr², where rrr is the radius)

For wires A and B:

​$$\frac{R_A}{R_B} = \frac{A_B}{A_A}$$​​

It is given that:

R_A=9R_B

This implies:

​$$\frac{A_B}{A_A} = 9$$​​

Since the area is proportional to the square of the radius:

​$$\frac{r_B^2}{r_A^2} = 9$$​​

Taking the square root of both sides:

​$$\frac{r_B}{r_A} = 3$$​​

Thus, the ratio of the radius of wire A to that of wire B is:

​$$rA:rB=1:3$$​​