A metallic wire having a resistance of 20 is cut into two eal parts in length. These parts are then connected in parallel. The resistance of this parallel combination is eal to

The resistance of a uniform metallic conductor is directly proportional to its length. When a wire with an initial resistance of 20 Ω is cut into two equal parts, the length of each part is halved, resulting in each piece having a resistance of 10 Ω. When these two 10 Ω resistors are connected in parallel, the equivalent resistance (Rp) is calculated using the reciprocal formula: 1/Rp = 1/R1 + 1/R2 [1][2]. For two equal resistors in parallel, the equivalent resistance is simply half the value of one resistor. Therefore, Rp = 10 Ω / 2 = 5 Ω. This follows the principle that the total resistance in a parallel combination is always less than the value of the smallest individual resistor.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186
2. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192