`In` an A.C. circuit the impedance is Z = `100 ` angle `30^(@) Omega` , then the resistance of the circuit in ohm will be

Options

A. 50
B. 100
C. `50sqrt(3)`
D. `100sqrt(3)`

Answer

To find the resistance of the circuit given the impedance in an AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The impedance \( Z \) is given as \( 100 \angle 30^\circ \, \Omega \).
- Here, \( Z = 100 \, \Omega \) and the phase angle \( \phi = 30^\circ \).

2. **Use the Relationship Between Impedance and Resistance**:
- The relationship between impedance \( Z \), resistance \( R \), and phase angle \( \phi \) in an AC circuit is given by:
\[ Z = R + jX \]
- The cosine of the phase angle is related to resistance and impedance as follows:
\[ \cos \phi = \frac{R}{Z} \]

3. **Rearrange the Formula to Find Resistance**:
- Rearranging the formula gives:
\[ R = Z \cdot \cos \phi \]

4. **Substitute the Known Values**:
- Substitute \( Z = 100 \, \Omega \) and \( \phi = 30^\circ \):
\[ R = 100 \cdot \cos(30^\circ) \]

5. **Calculate \( \cos(30^\circ) \)**:
- The value of \( \cos(30^\circ) \) is \( \frac{\sqrt{3}}{2} \).

6. **Perform the Calculation**:
- Substitute \( \cos(30^\circ) \) into the equation:
\[ R = 100 \cdot \frac{\sqrt{3}}{2} \]
- Simplifying this gives:
\[ R = 50\sqrt{3} \, \Omega \]

7. **Final Answer**:
- Therefore, the resistance of the circuit is:
\[ R = 50\sqrt{3} \, \Omega \]