In a series LCR circuit resistance `R = 10Omega` and the impedance `Z = 10 Omega` The phase difference between the current and the voltage is

Options

A. `0^@`
B. `30^@`
C. `45^@`
D. `60^@`

Answer

To find the phase difference between the current and the voltage in a series LCR circuit where the resistance \( R = 10 \, \Omega \) and the impedance \( Z = 10 \, \Omega \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between resistance, impedance, and phase difference**:
In an LCR circuit, the phase difference \( \phi \) between the current and voltage can be determined using the power factor, which is defined as:
\[ \text{Power Factor} = \cos \phi = \frac{R}{Z} \]

2. **Substitute the given values**:
Here, we know:
\[ R = 10 \, \Omega \quad \text{and} \quad Z = 10 \, \Omega \]
Therefore, substituting these values into the power factor equation gives:
\[ \cos \phi = \frac{10}{10} = 1 \]

3. **Determine the angle \( \phi \)**:
Since the power factor is equal to 1, we can find the phase difference \( \phi \) by taking the inverse cosine:
\[ \phi = \cos^{-1}(1) \]
The angle whose cosine is 1 is:
\[ \phi = 0^\circ \]

4. **Conclusion**:
The phase difference between the current and the voltage in the circuit is:
\[ \phi = 0^\circ \]

### Final Answer:
The phase difference between the current and the voltage is \( 0^\circ \).