In an `AC` circuit, the impedance is `sqrt3` times the reactance, then the phase angle is

Options

A. `60^@`
B. `30^@`
C. zero
D. none of these

Explanation

To solve the problem step by step, we will analyze the relationship between impedance (Z), reactance (X), and phase angle (φ) in an AC circuit.

### Step 1: Understand the relationship given in the problem
We are given that the impedance (Z) is equal to \(\sqrt{3}\) times the reactance (X). This can be expressed mathematically as:
\[ Z = \sqrt{3} X \]

### Step 2: Recall the impedance triangle
In an AC circuit, the impedance triangle relates the resistance (R), reactance (X), and impedance (Z). The triangle is formed as follows:
- The base represents the resistance (R).
- The perpendicular side represents the reactance (X).
- The hypotenuse represents the impedance (Z).

### Step 3: Use the definition of sine in the impedance triangle
From the impedance triangle, we can relate the sine of the phase angle (φ) to the reactance and impedance:
\[ \sin \phi = \frac{X}{Z} \]

### Step 4: Substitute the given relationship into the sine equation
Substituting \(Z = \sqrt{3} X\) into the sine equation, we get:
\[ \sin \phi = \frac{X}{\sqrt{3} X} \]
This simplifies to:
\[ \sin \phi = \frac{1}{\sqrt{3}} \]

### Step 5: Find the phase angle (φ)
To find the phase angle (φ), we take the inverse sine:
\[ \phi = \sin^{-1}\left(\frac{1}{\sqrt{3}}\right) \]

### Step 6: Calculate the value of φ
Using a calculator or trigonometric tables, we find:
\[ \phi \approx 35.26^\circ \]

### Step 7: Determine the correct option
The options given were 60°, 30°, 0°, and none of these. Since 35.26° is not listed among the options, the correct answer is:
**None of these.**

### Summary of the Solution
The phase angle (φ) in the given AC circuit is approximately 35.26°, which corresponds to the answer "none of these."

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