Electrical 82513

How long will it take for a current of 8A in a resistance of 30 ohms to develop thermal energy of 3 MJ if the efficiency of converting electrical energy into heat is 90%?

Correct answer:

t =  28.9 min

Step-by-step explanation:

$$\begin{gathered} I=8\text{A} \\ R=30\Omega \\ Q=3\cdot 1000\cdot 1000=3000000\text{J} \\ \eta =90\%=\frac{90}{100}=\frac{9}{10}=0.9 \\ Q=\eta \cdot P\cdot t \\ P=R\cdot I^2=30\cdot 8^2=1920\text{W} \\ {t}_1=Q/(\eta \cdot P)=3000000/(0.9\cdot 1920)=\frac{15625}{9}\doteq 1736.1111\text{s} \\ t=t_1\to \text{min}=t_1:60\text{min}=1736.1111:60\text{min}=28.9\text{min}=28.9\text{min} \end{gathered}$$

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