Join Sarthaks eConnect Today - Largest Online Education Community!
+2 votes
asked in Physics by (7.5k points)
A heater boils 1 kg of water in time t1 and another heater boils the same in time t2. If both the heaters are connected in parallel, the combination will boil the water in how much time?

1 Answer

+4 votes
answered by (13.4k points)
selected by
Best answer

We know that electric heater contain coils which have some resistances. So let R1 and R2 be the resistances of the two heaters respectively. The amount of heat required is the same in all the three cases given in the problem as it is required to heat the same amount of water i.e 1 kg. Let t be the time required to heat the water with the combination of heaters connected in parallel.

We know from Joule’s Law of Heating

Heat (H) = V2 x time(t) / R

H1 = V2 x t1/ R1
H2 = V2 x t2/ R2
H1 = H2 

Equating  H1 to H2 we get the relation R2 = t2R1 / t1.
Parallel combination of heaters: H3 = V2 x (R1 + R2) x t / R1R2
Equating H3 to H1 and substituting for R2 in terms of R1, we get

=> V2 x (R1 + R2) x t / R1R2 = V2 x t1/ R1
=> (R1 + R2) x t / R2 = t1

=> (R1 + t2R1/t1) x t / (t2R1 / t1) = t1
=> R1(1 + t2/t1) x t t1/ (t2R1) =  t1

Solving we get :

t = t1 t/ (t1 + t2)

So, If both the heaters are connected in parallel, the combination will boil the water in time

t = t1 t/ (t1 + t2)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon