Three wires of resistance 1 ohm, 2 ohm and 3 ohm respectively are connected in…
2016
Three wires of resistance 1 ohm, 2 ohm and 3 ohm respectively are connected in parallel. The equivalent resistance of the circuit is
- A.
6/11 ohm
- B.
11/6 ohm
- C.
6 ohm
- D.
1/6 ohm
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Correct answer: A
For resistors connected in parallel, the equivalent resistance is given by the reciprocal-sum rule: 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ... . Because each parallel branch adds another path for current, the equivalent resistance of a parallel combination is always smaller than the smallest individual resistor.
Here the three resistances are R1 = 1 ohm, R2 = 2 ohm, and R3 = 3 ohm.
Apply the parallel formula: 1/R_eq = 1/1 + 1/2 + 1/3.
Take the LCM of the denominators, which is 6: 1/R_eq = 6/6 + 3/6 + 2/6 = 11/6.
Invert the sum to get the equivalent resistance: R_eq = 6/11 ohm.
This checks out: 6/11 ohm is smaller than the smallest of the three resistors (1 ohm), exactly as the parallel-combination rule requires.