A wire of a given material has length ' l ' and resistance ' R '. Another wire of the same material having nine times the length and the same area of cross section will have a resistance equal to:

Correct option is C

​Let's analyze the relationship between resistance, length, and area of cross-section of a wire.​

Resistance (R) is directly proportional to length (L) and inversely proportional to the area of cross-section (A). This can be expressed as:  

​$$R \propto \frac{L}{A}$$​​

For two wires of the same material, the proportionality constant remains the same. So, we can write:

​$$\frac{R_1}{R_2} = \left( \frac{L_1}{L_2} \right) \times \left( \frac{A_2}{A_1} \right)$$​​

According to question:

​$$L_1 = l \\L_2 = 9l \\A_1 = A_2 \quad (\text{same area of cross-section})$$​​

Substituting these values:

​$$\frac{R_1}{R_2} = \left( \frac{l}{9l} \right) \times \left( \frac{A_2}{A_2} \right)$$

​​$$\frac{R_1}{R_2} = \frac{1}{9}$$​​

Therefore, $$R_2 = 9R_1$$​​