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Question

An electric kettle has two heating elements. One brings it to boil in 10 min and the other in 15 min. If two heating elements are connected in parallel, the water in kettle will boil in:

A
5 min
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B
6 min
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C
7 min
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D
25 min
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Solution

The correct option is B 6 min
Assumption: Both the heating elements are supplied with the same potential difference and same mass of water is heated.

Heat supplied is same for both the heating elements when connected individually. Using Joule's Law,
H1=H2
V2R1t1=V2R2t2
R2R1=t2t1=1510=1.5

When connected in parallel, net resistance is:
Rp=R1R2R1+R2
=1.5R12.5=0.6R1

Now, using Joule's law for combination,
H1=V2Rpt
V2R1t1=V20.6R1t
t=6 min

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