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Question

Heater-1, takes 3 minutes to boil a given amount of water. Heater-2 takes 6 minutes. If t1 and t2 are the time taken to boil the same amount of water, when the two heaters are connected in series and parallel, respectively, then t1t2=?

[Assume same cell is connected in all the cases]

A
92
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B
29
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C
49
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D
94
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Solution

The correct option is A 92
Here, the heat required (say H) to boil water is the same.

Let P1 and P2 are the powers of the heaters.

Then, H=P1t1=P2t2

So,
P1=Ht1=H3

P2=Ht2=H6

In series,

P=P1P2P1+P2(H3×H6)(H3+H6)=H9

Now,
t1=HP=H(H9)=9 minutes

In parallel,

P=P1+P2=H3+H6=H2

t2=HP=HH2=2 minutes

Further,

t1t2=92

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