QQuestion
Three equal resistors connected in series across a source of e.m.f. together dissipate 10 W of power. What would be the power dissipated if the same resistors were connected in parallel across the same source of e.m.f.?
✓Answer
Let each resistor be R.
When connected in series,
Equivalent resistance = 3R
Given, Power dissipated = 10 W
Using the formula, P = \frac{V^2}{R}
⇒ 10 = \frac{V^2}{3R}
⇒ V² = 10 × 3R = 30 R
When the same resistors are connected in parallel,
Equivalent resistance = \frac{R}{3}
Power (P) = \frac{V^2}{R/3} = \frac{3V^2}{R}
Substituting V² = 30R,
P = \frac{3 \times 30R}{R} = 90 W
Hence, the power dissipated in the parallel combination is 90 W.
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