Новое решение
en/11.1.28.md
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| + | ### Statement | ||
| + | |||
| + | $11.1.28.$ [Insert the problem statement] | ||
| + | |||
| + | ### Solution | ||
| + | |||
| + | It is known that the induced EMF of an electric motor is directly proportional to the magnetic flux and its frequency. Since only the motor's frequency varies, we could write the following: | ||
| + | |||
| + | \begin{equation} | ||
| + | \mathcal{E}_i=k\omega | ||
| + | \end{equation} | ||
| + | |||
| + | where $\mathcal{E}_i$ is the induced EMF, $\omega$ is angular frequency of the motor and $k$ is a constant. | ||
| + | |||
| + | |||
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| + | For the first case we have: | ||
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| + | |||
| + | \begin{equation} | ||
| + | \mathcal{E}_1+k\omega_1=IR | ||
| + | \end{equation} | ||
| + | |||
| + | |||
| + | where $ \mathcal{E}_1=24V $, $I=0.2$A,$R=20$$\Omega$ and $\omega_1=600\min^{-1}$ | ||
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| + | |||
| + | Similarly,for the second case we could write: | ||
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| + | |||
| + | \begin{equation} | ||
| + | \mathcal{E}_2+k\omega_2=0 | ||
| + | \end{equation} | ||
| + | |||
| + | |||
| + | where $\omega_2=1200\min^{-1}$ | ||
| + | |||
| + | |||
| + | By substituting $k$ from eq(2) to eq(3) we get the answer for $\mathcal{E}_2$: | ||
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| + | |||
| + | |||
| + | \begin{equation} | ||
| + | \mathcal{E}_2=(\mathcal{E}_1-IR)\frac{\omega_2}{\omega_1}=40V | ||
| + | \end{equation} | ||
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| + | #### Answer | ||
| + | |||
| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $11.1.28.$ [Insert the problem statement] | |||
| ### Solution | |||
| It is known that the induced EMF of an electric motor is directly proportional to the magnetic flux and its frequency. Since only the motor's frequency varies, we could write the following: | |||
| \begin{equation} | |||
| \mathcal{E}_i=k\omega | |||
| \end{equation} | |||
| where $\mathcal{E}_i$ is the induced EMF, $\omega$ is angular frequency of the motor and $k$ is a constant. | |||
| For the first case we have: | |||
| \begin{equation} | |||
| \mathcal{E}_1+k\omega_1=IR | |||
| \end{equation} | |||
| where $ \mathcal{E}_1=24V $, $I=0.2$A,$R=20$$\Omega$ and $\omega_1=600\min^{-1}$ | |||
| Similarly,for the second case we could write: | |||
| \begin{equation} | |||
| \mathcal{E}_2+k\omega_2=0 | |||
| \end{equation} | |||
| where $\omega_2=1200\min^{-1}$ | |||
| By substituting $k$ from eq(2) to eq(3) we get the answer for $\mathcal{E}_2$: | |||
| \begin{equation} | |||
| \mathcal{E}_2=(\mathcal{E}_1-IR)\frac{\omega_2}{\omega_1}=40V | |||
| \end{equation} | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||