In an amplitude modulator circuit the carrier wave is given by `C(t) = 4 sin(2 pi × 10^7 t)` while modulating signal is given by `m(t) = 2 sin(2 pi × 10^5 t)`. Then the bandwidth of the broadcast signal will be

Options

A. `0.2 MHZ`
B. `2 MHZ`
C. `20 MHZ`
D. `40 MHZ`

Answer

To find the bandwidth of the broadcast signal in an amplitude modulator circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Carrier and Modulating Frequencies**:
- The carrier wave is given by \( C(t) = 4 \sin(2 \pi \times 10^7 t) \).
- The modulating signal is given by \( m(t) = 2 \sin(2 \pi \times 10^5 t) \).
- From these equations, we can extract the frequencies:
- Carrier frequency \( f_c = 10^7 \) Hz.
- Modulating frequency \( f_m = 10^5 \) Hz.

2. **Apply the Bandwidth Formula for Amplitude Modulation**:
- The bandwidth \( B \) of an amplitude modulated signal is given by:
\[ B = 2 f_m \]
- This formula states that the bandwidth is twice the frequency of the modulating signal.

3. **Calculate the Bandwidth**:
- Substituting the value of \( f_m \):
\[ B = 2 \times 10^5 \text{ Hz} = 2 \times 10^5 \text{ Hz} \]

4. **Convert the Bandwidth to Megahertz**:
- To express the bandwidth in megahertz (MHz), we convert Hz to MHz:
\[ B = 2 \times 10^5 \text{ Hz} = 0.2 \text{ MHz} \]

5. **Final Result**:
- The bandwidth of the broadcast signal is \( 0.2 \) MHz.

### Final Answer:
The bandwidth of the broadcast signal is \( 0.2 \) MHz.

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