If the voltage in an ac circuit is reparesented by the equation `V=220 sqrt(2) sin (314 t - phi)`, calculate
frequency of ac

Options

A. `50 Hz`
B. `50 sqrt(2) Hz`
C. `50//sqrt(2) Hz`
D. `75 Hz`

Explanation

To calculate the frequency of the AC circuit represented by the equation \( V = 220 \sqrt{2} \sin(314t - \phi) \), we can follow these steps:

### Step 1: Identify the angular frequency (ω)
The given equation can be compared to the standard form of an AC voltage equation:
\[ V = V_0 \sin(\omega t + \phi) \]
From the equation \( V = 220 \sqrt{2} \sin(314t - \phi) \), we can identify that:
\[ \omega = 314 \, \text{radians/second} \]

### Step 2: Use the relationship between angular frequency and frequency
The relationship between angular frequency (ω) and frequency (f) is given by:
\[ \omega = 2\pi f \]
We can rearrange this formula to solve for frequency:
\[ f = \frac{\omega}{2\pi} \]

### Step 3: Substitute the value of ω into the frequency formula
Now, substituting the value of \( \omega = 314 \):
\[ f = \frac{314}{2\pi} \]

### Step 4: Calculate the value of f
Using \( \pi \approx 3.14 \):
\[ f = \frac{314}{2 \times 3.14} = \frac{314}{6.28} \approx 50 \, \text{Hz} \]

### Step 5: Conclusion
Thus, the frequency of the AC circuit is:
\[ f \approx 50 \, \text{Hz} \]

### Final Answer
The frequency of the AC circuit is **50 Hz**.

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