A 300W carrier is modulated to a depth 75%. The total power in the modulated wave is

Options

A. 200W
B. 284W
C. 320W
D. 384W

Explanation

To find the total power in a modulated wave, we can use the following formula:

\[ P_t = P_c \left(1 + \frac{\eta^2}{2}\right) \]

Where:
- \( P_t \) is the total power in the modulated wave.
- \( P_c \) is the power of the carrier wave.
- \( \eta \) is the modulation depth (expressed as a decimal).

**Step-by-step Solution:**

1. **Identify the given values:**
- Power of the carrier wave, \( P_c = 300 \) W
- Modulation depth, \( \eta = 75\% = 0.75 \)

2. **Substitute the values into the formula:**
\[ P_t = 300 \left(1 + \frac{(0.75)^2}{2}\right) \]

3. **Calculate \( \eta^2 \):**
\[ \eta^2 = (0.75)^2 = 0.5625 \]

4. **Calculate \( \frac{\eta^2}{2} \):**
\[ \frac{0.5625}{2} = 0.28125 \]

5. **Add 1 to the result:**
\[ 1 + 0.28125 = 1.28125 \]

6. **Multiply by the power of the carrier wave:**
\[ P_t = 300 \times 1.28125 = 384.375 \text{ W} \]

7. **Round off the result:**
Since power is typically expressed in whole numbers, we can round it to:
\[ P_t \approx 384 \text{ W} \]

Thus, the total power in the modulated wave is approximately **384 W**.