In a R, L, C circult, three elements is connected in series by an ac source. If frequency is less than resonating frequency then net impedance of the circuit will be

Options

A. capacitive
B. inductive
C. capacitive or inductive
D. pure resistive

Answer

To determine the net impedance of a series RLC circuit when the frequency is less than the resonant frequency, we can follow these steps:

### Step 1: Understand the Impedance Formula
The impedance \( Z \) of a series RLC 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.

### Step 2: Identify the Reactances
The inductive reactance \( X_L \) and capacitive reactance \( X_C \) are defined as:
\[ X_L = \omega L \]
\[ X_C = \frac{1}{\omega C} \]
where \( \omega = 2\pi f \) is the angular frequency and \( f \) is the frequency of the AC source.

### Step 3: Analyze the Condition of Frequency
Given that the frequency is less than the resonant frequency, we know:
\[ \omega < \omega_r \]
The resonant frequency \( \omega_r \) is given by:
\[ \omega_r = \frac{1}{\sqrt{LC}} \]
Since the frequency is less than the resonant frequency, it implies:
\[ X_L < X_C \]
This means that the circuit behaves more like a capacitive circuit.

### Step 4: Determine the Net Impedance
Since \( X_C > X_L \), we can express the impedance as:
\[ Z = \sqrt{R^2 + (X_C - X_L)^2} \]
This indicates that the net impedance is dominated by the capacitive reactance when the frequency is below the resonant frequency.

### Step 5: Conclusion
Thus, when the frequency is less than the resonant frequency, the net impedance of the circuit will be capacitive in nature.

### Final Answer
The net impedance of the circuit will be capacitive.

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