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 solve the problem of calculating the average voltage from the given AC voltage equation, we can follow these steps:

### Step 1: Identify the given voltage equation
The voltage in the AC circuit is given by:
\[ V = 220 \sqrt{2} \sin(314t - \phi) \]

### Step 2: Compare with the standard form
The standard form of the AC voltage equation is:
\[ V = V_0 \sin(\omega t + \phi) \]
From the given equation, we can identify:
- \( V_0 = 220 \sqrt{2} \)
- \( \omega = 314 \, \text{rad/s} \)
- \( \phi \) is the phase angle (not needed for average voltage calculation).

### Step 3: Use the formula for average voltage
The average voltage \( V_{av} \) for an AC circuit is given by the formula:
\[ V_{av} = \frac{2V_0}{\pi} \]

### Step 4: Substitute the value of \( V_0 \)
Now, substitute \( V_0 = 220 \sqrt{2} \) into the average voltage formula:
\[ V_{av} = \frac{2 \times 220 \sqrt{2}}{\pi} \]

### Step 5: Simplify the expression
Calculating the numerator:
\[ 2 \times 220 \sqrt{2} = 440 \sqrt{2} \]
Thus, the average voltage becomes:
\[ V_{av} = \frac{440 \sqrt{2}}{\pi} \]

### Step 6: Final calculation
To express the average voltage in a numerical form, we can approximate \( \sqrt{2} \approx 1.414 \):
\[ V_{av} \approx \frac{440 \times 1.414}{\pi} \]
Calculating this gives:
\[ V_{av} \approx \frac{622.08}{\pi} \]

### Conclusion
The average voltage \( V_{av} \) is approximately:
\[ V_{av} \approx \frac{622}{\pi} \, \text{volts} \]