The phase difference between the current and voltage of `LCR` circuit in series combination at resonance is

Options

A. `0`
B. `pi//2`
C. `pi`
D. `-pi`

Explanation

To find the phase difference between the current and voltage in a series LCR circuit at resonance, we can follow these steps:

### Step 1: Understand the LCR Circuit
An LCR circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. The behavior of the circuit is influenced by the inductive reactance (XL) and capacitive reactance (XC).

**Hint:** Recall that the inductive reactance is given by \(X_L = \omega L\) and the capacitive reactance is given by \(X_C = \frac{1}{\omega C}\).

### Step 2: Determine Resonance Condition
At resonance, the inductive reactance equals the capacitive reactance:
\[ X_L = X_C \]
This means:
\[ \omega L = \frac{1}{\omega C} \]

**Hint:** Resonance occurs when the frequency of the source matches the natural frequency of the circuit.

### Step 3: Calculate Impedance at Resonance
The impedance (Z) of the series LCR circuit is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
At resonance, since \(X_L = X_C\), we have:
\[ Z = \sqrt{R^2 + (0)^2} = R \]

**Hint:** Remember that at resonance, the circuit behaves like a purely resistive circuit.

### Step 4: Analyze Phase Difference
In a purely resistive circuit, the current and voltage are in phase. This means that the phase difference (\(\phi\)) between the current and voltage is:
\[ \phi = 0^\circ \]

**Hint:** Consider the relationship between current and voltage in resistive circuits.

### Conclusion
Thus, the phase difference between the current and voltage in a series LCR circuit at resonance is \(0^\circ\).

**Final Answer:** The phase difference is \(0^\circ\).

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