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