Three resistors, R1, R2 and R3, (R1 > R2 > R3), are connected to a battery of voltage V, such that the circuit generates maximum heat per unit time. Which one among the following is the correct circuit combination for this ?
- A.R1, R2 and R3 are connected in series combination
- B.R1, R2 and R3 are connected in parallel combination
- C.R1 and R3 are connected in parallel and R2 is connected in series to the combination
- D.R1 and R3 are connected in series and R2 is connected parallel to the combination
Correct answer
Explanation
The correct answer is B, R1, R2 and R3 are connected in parallel combination. Heat produced per unit time is the power, and with a fixed battery voltage the power is P = V²/R. So the circuit gives the most heat when its total resistance is the smallest, and the smallest possible resistance comes from joining all three resistors in parallel. In a parallel circuit, 1/R = 1/R1 + 1/R2 + 1/R3, and the total comes out less than even the smallest resistor, R3. Each resistor also gets the full voltage V, so each draws its largest possible current. This is why household appliances are wired in parallel. Option A is wrong because in series the resistances add up, R1 + R2 + R3, giving the largest resistance and therefore the least heat. Option C is wrong because adding R2 in series to the parallel pair makes the total more than R2, far above the all-parallel value. Option D is wrong because R2 in parallel with (R1 + R3) gives a total a little below R2, still higher than when all three are in parallel. Exam tip: at fixed voltage, P = V²/R, so least resistance (all in parallel) means most heat.
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