As the frequency of an alternating current increases, the impedance of the circuit

Options

A. increases continuously
B. decreases continuously
C. remains constant
D. none of these

Explanation

To solve the question regarding the relationship between the frequency of an alternating current (AC) and the impedance of the circuit, we can analyze the components involved in impedance.

### Step-by-Step Solution:

1. **Understanding Impedance**:
Impedance (Z) in an AC circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \( R \) is the resistance, \( X_L \) is the inductive reactance, and \( X_C \) is the capacitive reactance.

2. **Reactance Definitions**:
- The inductive reactance \( X_L \) is given by:
\[ X_L = 2\pi f L \]
where \( f \) is the frequency and \( L \) is the inductance.
- The capacitive reactance \( X_C \) is given by:
\[ X_C = \frac{1}{2\pi f C} \]
where \( C \) is the capacitance.

3. **Effect of Increasing Frequency**:
- As the frequency \( f \) increases:
- \( X_L \) increases because it is directly proportional to \( f \).
- \( X_C \) decreases because it is inversely proportional to \( f \).

4. **Analyzing Impedance**:
- At resonance, \( X_L = X_C \). As frequency increases beyond the resonant frequency:
- \( X_L \) becomes greater than \( X_C \).
- Thus, \( (X_L - X_C) \) increases, leading to an increase in impedance \( Z \).
- Conversely, if the frequency is below resonance, \( X_C \) is greater than \( X_L \), and as frequency increases, \( X_C \) decreases, which also leads to an increase in \( Z \).

5. **Conclusion**:
- Therefore, as the frequency of the AC increases, the impedance of the circuit does not remain constant or decrease; it generally increases.
- The answer to the question is that the impedance of the circuit **increases** as the frequency increases.

### Final Answer:
The impedance of the circuit **increases** as the frequency of the alternating current increases.