When turning at 1500 rev / min, a certain generator produces 100.0 V. What must be its frequency

step 1 Hi for this question. I want to find the frequency given that initial frequency and voltage are

When turning at 1500 rev / min, a certain generator produces...

When turning at $1500 \mathrm{rev} / \mathrm{min}$, a certain generator produces $100.0$ V. What must be its frequency in rev/min if it is to produce $120.0$ V? Because the amplitude of the emf is proportional to the frequency, we have, for two frequencies $f_{1}$ and $f_{2}$, $$ \frac{\delta_{1}}{\delta_{2}}=\frac{f_{1}}{f_{2}} \quad \text { or } \quad f_{2}=f_{1} \frac{\delta_{2}}{\varepsilon_{1}}=(1500 \mathrm{rev} / \min )\left(\frac{120.0 \mathrm{~V}}{100.0 \mathrm{~V}}\right)=1800 \mathrm{rev} / \mathrm{min} $$

When turning at $1500 \mathrm{rev} / \mathrm{min}$, a certain generator produces $100.0$ V. What must be its frequency in rev/min if it is to produce $120.0$ V?
Because the amplitude of the emf is proportional to the frequency, we have, for two frequencies $f_{1}$ and $f_{2}$,
$$
\frac{\delta_{1}}{\delta_{2}}=\frac{f_{1}}{f_{2}} \quad \text { or } \quad f_{2}=f_{1} \frac{\delta_{2}}{\varepsilon_{1}}=(1500 \mathrm{rev} / \min )\left(\frac{120.0 \mathrm{~V}}{100.0 \mathrm{~V}}\right)=1800 \mathrm{rev} / \mathrm{min}
$$

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Key Concepts

Electromagnetic Induction

This concept refers to the process by which a changing magnetic field within a conductor produces an electromotive force (emf). It is the fundamental principle behind generators, where mechanical rotation creates a time-varying magnetic flux that induces voltage.

Relationship Between Rotational Speed and Induced emf

In electrical generators, the magnitude of the induced emf is directly related to the frequency of rotation, which corresponds to how rapidly the magnetic flux changes. An increase in rotational speed results in a proportionate increase in the induced emf, establishing a linear relationship between them.

Proportional Reasoning

This concept involves understanding that when one variable changes, another variable changes by the same proportional factor. In the context of the generator, if the frequency (or rotational speed) increases by a certain factor, the amplitude of the induced voltage increases by the same factor, allowing for predictions of voltage output based on changes in frequency.

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