Three equal resistors are connected in parallel configuration in a closed electrical circuit. Then the total resistance in the circuit becomes
- A.one-third of the individual resistance.
- B.two-third of the individual resistance.
- C.equal to the individual resistance.
- D.three times of the individual resistance.
Correct answer
Explanation
The correct answer is A, one-third of the individual resistance. For three equal resistors R in parallel, 1/Rp = 1/R + 1/R + 1/R = 3/R, so Rp = R/3.
In a parallel connection every resistor gets the same voltage, and the current divides among the branches. Adding a branch gives the current one more path, so the total resistance falls and is always less than the smallest single resistor. For n equal resistors in parallel the total is R/n; three resistors of 6 ohms each give 2 ohms. In series the same three would add up to 3R, or 18 ohms. House wiring uses parallel circuits so that every appliance gets the full mains voltage and can be switched on and off on its own.
B is wrong because two-thirds would need a different mix, not three equal resistors in parallel. C is wrong because adding parallel paths always lowers resistance. D is wrong because three times the resistance is the series result.
Exam tip: n equal resistors give nR in series and R/n in parallel.
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