An ac generator gives an output voltage of E= 170 sin 56.52t. What is the frequency of alternating voltage produced?

Answer

To find the frequency of the alternating voltage produced by the AC generator given the output voltage equation \( E = 170 \sin(56.52t) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given equation**: The output voltage is given as:
\[ E = 170 \sin(56.52t) \]

2. **Compare with the standard form**: The standard form of the output voltage for an AC generator is:
\[ E = E_0 \sin(\omega t) \]
where \( E_0 \) is the maximum voltage and \( \omega \) is the angular frequency.

3. **Extract the angular frequency**: From the given equation, we can see that:
\[ \omega = 56.52 \, \text{rad/s} \]

4. **Relate angular frequency to frequency**: The relationship between angular frequency \( \omega \) and frequency \( f \) is given by:
\[ \omega = 2\pi f \]

5. **Solve for frequency**: Rearranging the equation to solve for \( f \):
\[ f = \frac{\omega}{2\pi} \]
Substituting the value of \( \omega \):
\[ f = \frac{56.52}{2\pi} \]

6. **Calculate the frequency**: Now we can calculate the frequency:
\[ f \approx \frac{56.52}{6.2832} \approx 9 \, \text{Hz} \]

### Final Answer:
The frequency of the alternating voltage produced is approximately \( 9 \, \text{Hz} \).

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