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  • Two different coils have self-inductance<img alt="\mathrm{ L_{1} = 8 mH, L_{2} = 2mH}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20L_%7B1%7D%20%3D%208%20mH%2C%20L_%7B2%7D%20

Two different coils have self-inductance\mathrm{ L_{1} = 8 mH, L_{2} = 2mH}. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coils are\mathrm{ i_{1}, V_{1}} and \mathrm{ w_{1}} respectively. Corresponding values for the second coil at that instant ratei_{2}, V_{2} and \mathrm{w_{2}} respectively. Then which of the following is wrong:

Option: 1

\mathrm{\frac{\mathrm{i}_1}{\mathrm{i}_2}=\frac{1}{4}} 


Option: 2

\mathrm{\frac{i_1}{i_2}=4}


Option: 3

\mathrm{\frac{\mathrm{w}_2}{\mathrm{w}_1}=4}


Option: 4

\mathrm{\frac{\mathrm{V}_2}{\mathrm{~V}_1}=\frac{1}{4}}


Answers (1)

best_answer

 \begin{aligned} & \mathrm{e}=\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}} \\ & \mathrm{e} \propto \mathrm{L} \end{aligned}

So

\frac{\mathrm{e}_1}{\mathrm{e}_2}=\frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{8}{2}=\frac{4}{1}

\text { Since } \mathrm{P}=\mathrm{ei}=\text { Constant }

Therefore

\begin{aligned} &\frac{\mathrm{di}_1}{\mathrm{dt}}=\frac{\mathrm{di}_2}{\mathrm{dt}}\\ &\mathrm{P}_1=\mathrm{P}_2=\mathrm{P}\\ &e_1 i_1=e_2 i_2\\ &\therefore \frac{i_1}{i_2}=\frac{e_2}{e_1}=\frac{1}{4} \end{aligned}

 

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Sayak

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