If modulation index `mu= 1/2` and `V_(2) = 2` then `V_(C) = ?`

Options

A. 4
B. 2
C. 6
D. 8

Explanation

To solve the problem, we need to find the carrier signal voltage \( V_c \) given the modulation index \( \mu \) and the modulating signal voltage \( V_m \).

### Step-by-Step Solution:

1. **Understand the given values:**
- Modulation index \( \mu = \frac{1}{2} \)
- Modulating signal voltage \( V_m = 2 \)

2. **Recall the formula for modulation index:**
The modulation index \( \mu \) is defined as:
\[ \mu = \frac{V_m}{V_c} \]
where \( V_m \) is the modulating signal voltage and \( V_c \) is the carrier signal voltage.

3. **Rearrange the formula to find \( V_c \):**
We can rearrange the formula to express \( V_c \) in terms of \( V_m \) and \( \mu \):
\[ V_c = \frac{V_m}{\mu} \]

4. **Substitute the known values into the equation:**
Now, substituting the values of \( V_m \) and \( \mu \):
\[ V_c = \frac{2}{\frac{1}{2}} \]

5. **Simplify the expression:**
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ V_c = 2 \times 2 = 4 \]

6. **Conclusion:**
Thus, the carrier signal voltage \( V_c \) is:
\[ V_c = 4 \]

### Final Answer:
The value of \( V_c \) is 4.

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