Two metallic wires made from copper have same length but the radius of wire 1 is half of that of wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes

The resistance of a metallic conductor is directly proportional to its length and inversely proportional to its cross-sectional area [4]. Since both copper wires have the same length and material, their resistance depends solely on the area (A = πr²). Wire 1 has a radius half that of wire 2 (r1 = 0.5r2), meaning its area is one-fourth that of wire 2 (A1 = A2/4). Consequently, the resistance of wire 1 (R) is four times the resistance of wire 2 (R2), so R2 = R/4. When resistors are connected in series, the total resistance is the sum of individual resistances [4]. Therefore, the total resistance is R + R/4, which equals 1.25R or 5R/4. Option 2 is selected as the placeholder for this calculated value.

Sources

1. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Solution > p. 184
2. [4] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > 11.6 RESISTANCE OF A SYSTEM OF RESISTORS > p. 181
3. [3] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192