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

Options

A. 220 V
B. `622 // (pi V)`
C. `220//sqrt(2) V`
D. `200 sqrt(2) V`

Explanation

To calculate the average voltage from the given AC voltage equation \( V = 220 \sqrt{2} \sin(314t - \phi) \), we can follow these steps:

### Step 1: Identify the Peak Voltage
The given voltage equation is in the form \( V = V_0 \sin(\omega t - \phi) \), where:
- \( V_0 = 220 \sqrt{2} \) (the peak voltage)

### Step 2: Use the Formula for Average Voltage
The average voltage \( V_{\text{average}} \) for an AC circuit can be calculated using the formula:
\[ V_{\text{average}} = \frac{2}{\pi} V_0 \]

### Step 3: Substitute the Peak Voltage into the Formula
Now, substitute the value of \( V_0 \) into the average voltage formula:
\[ V_{\text{average}} = \frac{2}{\pi} (220 \sqrt{2}) \]

### Step 4: Calculate the Average Voltage
Now, we will calculate the average voltage:
\[ V_{\text{average}} = \frac{2 \times 220 \sqrt{2}}{\pi} \]
Calculating \( 2 \times 220 \sqrt{2} \):
\[ 2 \times 220 = 440 \]
Thus,
\[ V_{\text{average}} = \frac{440 \sqrt{2}}{\pi} \]

### Step 5: Final Result
The average voltage is:
\[ V_{\text{average}} = \frac{440 \sqrt{2}}{\pi} \text{ volts} \]