Suppose voltage V is applied across resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case will be
- A.P
- B.3P
- C.P/3
- D.2P/3
Correct answer
Explanation
The correct answer is B, 3P. Three equal resistors R in parallel have a combined resistance of R/3, and at the same voltage the power, V²/R, becomes three times as large.
In the first case the power is P = V²/R. For resistors in parallel, 1/Rp = 1/R + 1/R + 1/R = 3/R, so Rp = R/3. With the same voltage, the new power is V² ÷ (R/3) = 3V²/R = 3P. Another way to see it: each resistor still has the full voltage V across it, so each dissipates P, and the three together give 3P. The circuit draws three times the current from the source.
Option A is wrong because P is the power of only one of the three resistors. Option C is wrong because P/3 is what three resistors in series would give at the same voltage. Option D is wrong because 2P/3 does not follow from any of these combinations.
Exam tip: at a fixed voltage, n equal resistors in parallel give nP and in series give P/n.
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