First slide

Electrical power

Question

One filament takes 10 min to heat a kettle and another takes 15 min. If connected in parallel, they combindly take ______ min to heat the same kettle.

Moderate

A

6
B

12.5
C

25
D

7.5

Solution

Lets suppose E energy is required to heat the kettle and P₁ and P₂ are the power of filament which take 10 min and 15 min respectively to heat the kettle. So $P_{1} = \frac{E}{10}$ and $P_{2} = \frac{E}{15} .$ Now both the filaments are connected in parallel to heat the same kettle hence their combined power will be (P₁ + P₂) but the energy required is still E. If the time they take is t then $(P_{1} + P_{2}) t = E \Rightarrow (\frac{E}{10} + \frac{E}{15}) t = E$ $\Rightarrow \frac{5 E}{30} \times t = E \Rightarrow t = 6 \min$

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