If the peak value of an alternating emf is 15V, what is its mean value over half cycle?

Answer

To find the mean value of an alternating EMF over half a cycle, we can follow these steps:

### Step 1: Understand the given information
We are given the peak value of the alternating EMF, denoted as \( E_0 = 15 \, V \).

### Step 2: Recall the formula for mean value over half cycle
The mean (average) value of an alternating EMF over half a cycle can be calculated using the formula:
\[ E_{\text{avg}} = \frac{2}{\pi} E_0 \]
This formula is derived from the integral of the sine wave over half a cycle.

### Step 3: Substitute the peak value into the formula
Now, we will substitute the peak value \( E_0 = 15 \, V \) into the formula:
\[ E_{\text{avg}} = \frac{2}{\pi} \times 15 \]

### Step 4: Calculate the mean value
Now, we can calculate the value:
\[ E_{\text{avg}} = \frac{30}{\pi} \]
Using the approximate value of \( \pi \approx 3.14 \):
\[ E_{\text{avg}} \approx \frac{30}{3.14} \approx 9.55 \, V \]

### Step 5: Final result
Thus, the mean value of the alternating EMF over half a cycle is approximately:
\[ E_{\text{avg}} \approx 9.55 \, V \]