In a circuit containing R and L , as the frequency of the impressed AC increase, the impedance of the circuit

Options

A. decreases
B. increases
C. remains unchanged
D. first increases and then decreases

Explanation

To solve the question regarding the impedance of a circuit containing a resistor (R) and an inductor (L) as the frequency of the impressed AC increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Impedance**:
The impedance (Z) of an R-L circuit is given by the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
where \(X_L\) is the inductive reactance.

2. **Inductive Reactance**:
The inductive reactance \(X_L\) is defined as:
\[ X_L = \omega L = 2\pi f L \]
where \(f\) is the frequency of the AC source and \(L\) is the inductance.

3. **Substituting Inductive Reactance**:
By substituting \(X_L\) into the impedance formula, we get:
\[ Z = \sqrt{R^2 + (2\pi f L)^2} \]

4. **Analyzing the Effect of Frequency**:
As the frequency \(f\) increases, the term \(2\pi f L\) also increases. Therefore, the expression for impedance becomes:
\[ Z = \sqrt{R^2 + (2\pi f L)^2} \]
This indicates that as \(f\) increases, the value of \((2\pi f L)^2\) increases, leading to an increase in the overall impedance \(Z\).

5. **Conclusion**:
Since the impedance \(Z\) increases with an increase in frequency \(f\), we can conclude that the impedance of the circuit increases as the frequency of the impressed AC increases.

### Final Answer:
The impedance of the circuit increases as the frequency of the impressed AC increases.