An electricity and magnetism problem by sakshi rathore

Electricity and Magnetism Level 2

An electric stove boils 1 kg water in 2 min and an another stove boils 1 kg water in 3 min. If the voltage of both stoves is equal and are joined in parallel, find the time it takes to boil the water.

2.4 5 12 1.2

Sakshi Rathore by sakshi rathore , 21, USA

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1 solution

Chew-Seong Cheong
Jul 18, 2015

Let the energy needed to boil 1 kg of water be E E , and the powers of stove 1 and stove 2 be P 1 P_1 and P 2 P_2 respectively. Then the power of two stoves in parallel is P 1 + P 2 P_1 + P_2 . Then we have:

{ 2 P 1 = E ⇒ P 1 = E 2 3 P 2 = E ⇒ P 2 = E 3 \begin{cases} 2P_1 = E & \Rightarrow P_1 = \dfrac{E}{2} \\ 3P_2 = E & \Rightarrow P_2 = \dfrac{E}{3} \end{cases}

If it takes the two stoves in parallel t t minutes to boil 1 kg of water, then:

t = E P 1 + P 2 = E E 2 + E 3 = 1 1 2 + 1 3 = 1 5 6 = 6 5 = 1.2 t = \dfrac{E}{P_1+P_2} = \dfrac{E}{\frac{E}{2} + \frac{E}{3}} = \dfrac{1}{\frac{1}{2} + \frac{1}{3}} = \dfrac{1}{\frac{5}{6}} = \dfrac{6}{5} = \boxed{1.2} min.

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Moderator note:

A very clear approach.

Can you say me why Energy (E) is constant?

Shiny Maddi - 3 years, 8 months ago

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The energy to boil 1 kg of water is experimentally shown to be constant for an atmospheric pressure. It is called the latent energy of water. It is 2264.705 kJ/kg at standard atmospheric pressure and boiling point of 100 ∘ ^\circ C.

Chew-Seong Cheong - 3 years, 8 months ago

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