Question

Calculate the amount of heat produced per second when a bulb of $ 50{\text{W}} $ , $ 200{\text{V}} $ glows assuming only $ 20\% $ of the electric energy is converted into light.
(A) $ 20{\text{J}} $
(B) $ 40{\text{J}} $
(C) $ 50{\text{J}} $
(D) $ 200{\text{J}} $

Answer 1

Hint : To solve this question, we need to use the formula of the energy in terms of the power to find out the electrical energy generated by the bulb. Then using the percentage given in the question, we can find out the percentage of electric energy converted into heat, from which we can get the required amount of the heat produced.

Formula used: The formula used to solve this question is given by
 $ E = Pt $ , here $ E $ is the electric energy produced by a power of $ P $ in time $ t $ .

Complete step by step answer
The rating of the bulb is given as $ 50{\text{W}} $ , $ 200{\text{V}} $ . This means that the given bulb requires a power of $ 50{\text{W}} $ to work. We know that the energy is related to the power by the formula
 $ E = Pt $
According to the question, the time $ t = 1s $ . Also, power required by the bulb is $ P = 50{\text{W}} $ . Substituting these above, we get
 $ E = 50 \times 1{\text{J}} $
 $ \Rightarrow E = 50{\text{J}} $ (1)
So the electric energy produced by the bulb is equal to $ 50{\text{J}} $ .
We know that the bulb along with glowing also generates heat. So it produces two kinds of energy; one is light energy, and the other one is heat.
According to the question, the bulb converts only $ 20\% $ of the electric energy into light. This means that the rest $ 80\% $ of the electric energy is converted into heat. Therefore the heat generated is given by
 $ H = 0.8E $
From (1)
 $ H = 0.8 \times 50{\text{J}} $
 $ \Rightarrow H = 40{\text{J}} $
Thus the amount of heat produced by the bulb is equal to $ 40{\text{J}} $ .
Hence, the correct answer is option B.

Note
We should not directly use the percentage given in the question to calculate the heat generated. The percentage is given for the light energy generated by the bulb, and not for the heat.