An electric wire of resistance 50 ohm is cut into five equal wires. These wires are then connected in parallel. What is the equivalent resistance of this combination?

The resistance of a conductor is directly proportional to its length [2]. When a wire with a total resistance of 50 ohms is cut into five equal parts, the length of each piece becomes one-fifth of the original length. Consequently, the resistance of each individual piece is 50/5 = 10 ohms [1]. When these five resistors are connected in parallel, the reciprocal of the equivalent resistance (Rp) is the sum of the reciprocals of the individual resistances [2]. The formula is 1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5. Substituting the values, 1/Rp = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10 = 1/2. Therefore, the equivalent resistance Rp is 2 ohms [1]. This confirms that the total resistance in a parallel circuit is always less than the smallest individual resistor.

Sources

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