In a series `LCR` circuit, resistance `R=10Omega` and the impedence `Z=20Omega` the phase difference between the current and the voltage is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Explanation

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

### Step-by-Step Solution:

1. **Identify Given Values**:
- Resistance \( R = 10 \, \Omega \)
- Impedance \( Z = 20 \, \Omega \)

2. **Understand the Relationship**:
- The phase difference \( \phi \) between the current and voltage in an LCR circuit can be found using the formula for the power factor:
\[ \text{Power Factor} = \cos \phi = \frac{R}{Z} \]

3. **Calculate the Power Factor**:
- Substitute the given values into the formula:
\[ \cos \phi = \frac{R}{Z} = \frac{10}{20} = \frac{1}{2} \]

4. **Find the Phase Difference**:
- To find \( \phi \), we take the inverse cosine:
\[ \phi = \cos^{-1}\left(\frac{1}{2}\right) \]

5. **Determine the Angle**:
- The angle whose cosine is \( \frac{1}{2} \) is:
\[ \phi = 60^\circ \]

### Final Answer:
The phase difference between the current and the voltage is \( 60^\circ \).

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