For good demodulation of AM signal of carrier frequency f, the value of RC should be

Options

A. `1/f`
B. `lt (1)/(f) `
C. `ge (1)/(f) `
D. `gt gt (1)/(f) `

Explanation

To determine the appropriate value of the time constant \( RC \) for good demodulation of an AM signal with carrier frequency \( f \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Components**:
- An AM signal consists of a carrier wave and the modulated information. The carrier frequency is denoted as \( f \).
- The demodulation circuit typically includes a diode, a capacitor, and a resistor.

2. **Circuit Configuration**:
- The diode rectifies the AM signal, allowing only the positive half-cycles to pass.
- The capacitor is used to smooth out the rectified signal, while the resistor helps in discharging the capacitor.

3. **Reactance of the Capacitor**:
- The reactance \( X_c \) of the capacitor is given by the formula:
\[ X_c = \frac{1}{2\pi f_c} \]
- Here, \( f_c \) is the carrier frequency.

4. **Condition for Good Demodulation**:
- For effective filtering of the high-frequency components from the AM signal, the reactance of the capacitor must be much smaller than the resistance \( R \):
\[ X_c \ll R \]
- This implies:
\[ \frac{1}{2\pi f_c} \ll R \]

5. **Rearranging the Inequality**:
- Rearranging the above inequality gives:
\[ R \gg \frac{1}{2\pi f_c} \]
- This can be rewritten in terms of the time constant \( RC \):
\[ RC \gg \frac{1}{f} \]

6. **Conclusion**:
- Therefore, for good demodulation of an AM signal of carrier frequency \( f \), the value of \( RC \) should be:
\[ RC \gg \frac{1}{f} \]
- This indicates that the time constant \( RC \) must be much greater than \( \frac{1}{f} \).

### Final Answer:
The value of \( RC \) should be greater than \( \frac{1}{f} \) for good demodulation of an AM signal.

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