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

Options

A. 220 V
B. 314 V
C. `220 sqrt(2) V`
D. `200//sqrt(2) V`

Explanation

To solve the problem of calculating the RMS value of the voltage represented by the equation \( V = 220 \sqrt{2} \sin(314t - \phi) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Form of the Voltage Equation**:
The given voltage equation is \( V = 220 \sqrt{2} \sin(314t - \phi) \). This can be compared to the standard form of an AC voltage equation, which is \( V = V_0 \sin(\omega t + \phi) \).

2. **Extract the Amplitude**:
From the equation, we can identify the amplitude \( V_0 \):
\[ V_0 = 220 \sqrt{2} \text{ volts} \]

3. **Understand the RMS Value Formula**:
The RMS (Root Mean Square) value of an AC voltage is calculated using the formula:
\[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \]

4. **Substitute the Amplitude into the RMS Formula**:
Now, substitute the value of \( V_0 \) into the RMS formula:
\[ V_{\text{rms}} = \frac{220 \sqrt{2}}{\sqrt{2}} \]

5. **Simplify the Expression**:
The \( \sqrt{2} \) in the numerator and denominator cancels out:
\[ V_{\text{rms}} = 220 \text{ volts} \]

6. **Conclusion**:
Therefore, the RMS value of the voltage is:
\[ V_{\text{rms}} = 220 \text{ volts} \]

### Final Answer:
The RMS value of the voltage is **220 volts**.

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