What is true in L.C.R. series circuit at a frequency less than resonant frequency:-
(a) I, lags E
(b) Circuit nature `to` capacitance
(c) Net reactance `to ` negative
(d) Power factor is of leading nature

Options

A. b& c
B. a,b,d
C. b,c,d
D. a,c,d

Answer

To solve the question regarding the behavior of an LCR series circuit at a frequency less than the resonant frequency, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Resonant Frequency**:
- The resonant frequency \( f_0 \) of an LCR circuit is given by the formula:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
- At resonant frequency, the inductive reactance \( X_L \) equals the capacitive reactance \( X_C \).

2. **Behavior Below Resonant Frequency**:
- When the frequency \( f \) is less than the resonant frequency \( f_0 \), the capacitive reactance \( X_C \) (which is \( \frac{1}{\omega C} \)) increases, and the inductive reactance \( X_L \) (which is \( \omega L \)) decreases.
- Therefore, \( X_C > X_L \).

3. **Circuit Nature**:
- Since \( X_C > X_L \), the circuit behaves like a capacitive circuit. This means that the overall reactance is capacitive in nature.

4. **Current and Voltage Phase Relationship**:
- In a capacitive circuit, the current leads the voltage. Therefore, the current \( I \) lags behind the voltage \( E \) (which is incorrect in this context).

5. **Net Reactance**:
- The net reactance \( X \) of the circuit can be expressed as:
\[ X = X_C - X_L \]
- Since \( X_C > X_L \), the net reactance \( X \) is positive, indicating that the circuit is capacitive.

6. **Power Factor**:
- The power factor \( \cos \phi \) is positive when the current leads the voltage, indicating a leading power factor.

### Conclusion:
Based on the analysis:
- **(a)** I lags E: **False** (current leads voltage in a capacitive circuit).
- **(b)** Circuit nature to capacitance: **True** (the circuit behaves like a capacitor).
- **(c)** Net reactance to negative: **False** (net reactance is positive).
- **(d)** Power factor is of leading nature: **True** (current leads voltage).

### Correct Options:
- The correct statements are **(b)** and **(d)**.