# An electric kettle has two coils. When one coil is switched an it takes 5 minutes to boil water and when second coil is switched on it takes 10 mi

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An electric kettle has two coils. When one coil is switched an it takes 5 minutes to boil water and when second coil is switched on it takes 10 minutes .How long will it take to boil water, when both the coil are used in series ?

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Correct Answer - 15 min
Let R_(1) ,R_(2) be the resistance of the two coils , V be the supply voltage and H be the heat required to boil the water
For the first coil H = (V^(2)t_(1))/(JR_(1)) = (V^(2) xx (5 xx 60))/(4.2 xx R_(1)) cel
For the second coil
H = (V^(2)t_(2))/(JR_(2))= (V^(2)xx 10 xx 60)/(4.2 xx R_(2)) cal
:. (V^(2) xx 5 xx 60)/(4.2 R_(1)) = (V^(2) xx 10 xx 60 )/(4.2 xx R_(2) or (R_(2))/(R_(1)) = (10)/(5) = 2
when the coil are connected in series the effective resistance R = R_(1) + R_(2)
Let r be the time in min boiling water , then
H = (V^(2)t)/(J(R_(1) + R_(2))) = (V^(2) xx t_(1))/(JR_(1))
or t = (t_(1)(R_(1) + R_(2)))/(R_(1)) = t_(1) ( 1 + (R_(2))/(R_(1))) = 5 ( 1+ 2) = 15 min