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Q62 (NDA-I/2010) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

The effective resistance of three equal resistances, each of resistance r, connected in parallel, is

Result
Your answer: —  Â·  Correct: B
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. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186
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