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 — A, one-third of the individual resistance. For resistors in parallel the reciprocals add: 1/R_total = 1/R + 1/R + 1/R = 3/R, so R_total = R/3. Three equal resistors in parallel therefore give an equivalent resistance one-third of a single one, because the extra parallel paths offer more routes for the current and lower the overall resistance. Adding resistors in parallel always brings the total below the smallest branch.
- (b)two-third of the individual resistance. — The reciprocal sum gives R/3, not 2R/3; no standard parallel combination of three equal resistors yields two-thirds.
- (c)equal to the individual resistance. — A parallel connection lowers the resistance below any single resistor, so it cannot stay equal to R.
- (d)three times of the individual resistance. — Three equal resistors give 3R only in series; in parallel the resistance falls to R/3, the opposite effect.
When resistors are joined in parallel, the same voltage acts across each and the reciprocal of the total resistance equals the sum of the reciprocals of the branches. For equal resistors this makes the combined resistance smaller than any single one.
A useful rule of thumb is that parallel lowers resistance while series raises it. For n equal resistors in parallel the total is R divided by n, so three give R/3, and the three-times answer is the series result, which is the classic trap.
- In parallel, 1/R_total = 1/R₁ + 1/R₂ + 1/R₃.
- For three equal resistors, 1/R_total = 3/R, so R_total = R/3.
- A parallel combination always gives a resistance smaller than the smallest branch.
- The same three resistors in series would instead give 3R.
Three equal resistors in parallel give one-third of the single resistance.
- Using the series formula, adding the resistances, for a parallel circuit.
- Forgetting that parallel resistance is always less than the smallest resistor.
Asked for the equivalent of three equal resistors in parallel; apply 1/R_total = 3/R to get R/3.
No directly related past PYQ was found.
- practice — not a real PYQ
Two equal resistors R are connected in parallel. Their equivalent resistance is
- (a)2R
- (b)R
- (c)R/2
- (d)R/4
Answer(c) R/2 — for two equal resistors in parallel the total halves.
- practice — not a real PYQ
Three resistors of 6 Ω each are connected in parallel. The equivalent resistance is
- (a)18 Ω
- (b)6 Ω
- (c)3 Ω
- (d)2 Ω
Answer(d) 2 Ω — 6 Ω divided by three.