Question map
The effective resistance of three equal resistances, each of resistance r, connected in parallel, is
Explanation
When resistors are connected in parallel, the reciprocal of the equivalent resistance (Rp) is equal to the sum of the reciprocals of the individual resistances [1][c5]. The general formula is 1/Rp = 1/R1 + 1/R2 +... + 1/Rn [t5]. For three resistors, each having a resistance of 'r', the equation becomes 1/Rp = 1/r + 1/r + 1/r [t2]. This simplifies to 1/Rp = 3/r. Taking the reciprocal to find the effective resistance, we get Rp = r/3 [t2][t3]. This demonstrates that for 'n' identical resistors in parallel, the equivalent resistance is the individual resistance divided by the number of paths (r/n) [t2][t8]. Consequently, for three equal resistors, the effective resistance is exactly one-third of the individual resistance, making option 2 the correct choice.
Sources
- [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186