A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be :

Options

A. 7 V
B. 11.2 V
C. 28 V
D. 22.4 V

Answer

To solve the problem, we need to find the peak voltage of the modulating signal (Vm) given the peak voltage of the carrier wave (Vc) and the modulation index (m).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Peak voltage of the carrier wave (Vc) = 14 V
- Modulation index (m) = 80% = 0.8

2. **Recall the Formula for Modulation Index:**
The modulation index (m) is defined as the ratio of the peak voltage of the modulating signal (Vm) to the peak voltage of the carrier wave (Vc):
\[ m = \frac{V_m}{V_c} \]

3. **Rearrange the Formula to Solve for Vm:**
From the formula, we can express Vm in terms of m and Vc:
\[ V_m = m \times V_c \]

4. **Substitute the Known Values:**
Now, substitute the known values into the equation:
\[ V_m = 0.8 \times 14 \, \text{V} \]

5. **Calculate Vm:**
Perform the multiplication:
\[ V_m = 11.2 \, \text{V} \]

6. **Conclusion:**
The peak voltage of the modulating signal (Vm) required to achieve a modulation index of 80% is 11.2 V.

### Final Answer:
The peak voltage of the modulating signal is **11.2 V**.