A coil of inductive reactance `1//sqrt(3)Omega` and resistance `1Omega` is connected to a `200V`, `50Hz` A.C. supply. The time lag between maximum voltage and current is

Options

A. `1/200s`
B. `1/300s`
C. `1/500s`
D. `1/600s`

Answer

To solve the problem step by step, follow these instructions:

### Step 1: Identify Given Values
- Inductive reactance, \( X_L = \frac{1}{\sqrt{3}} \, \Omega \)
- Resistance, \( R = 1 \, \Omega \)
- Voltage, \( V = 200 \, V \)
- Frequency, \( f = 50 \, Hz \)

### Step 2: Calculate the Phase Difference
The phase difference \( \phi \) between the voltage and the current in an R-L circuit can be calculated using the formula:

\[ \tan \phi = \frac{X_L}{R} \]

Substituting the values:

\[ \tan \phi = \frac{\frac{1}{\sqrt{3}}}{1} = \frac{1}{\sqrt{3}} \]

### Step 3: Find the Angle \( \phi \)
To find the angle \( \phi \), we take the arctangent:

\[ \phi = \tan^{-1}\left(\frac{1}{\sqrt{3}}\right) \]

From trigonometric values, we know:

\[ \phi = 30^\circ \]

### Step 4: Convert the Angle to Radians
Convert \( \phi \) from degrees to radians for further calculations:

\[ \phi = 30^\circ = \frac{\pi}{6} \, \text{radians} \]

### Step 5: Calculate Angular Frequency \( \omega \)
The angular frequency \( \omega \) is given by:

\[ \omega = 2\pi f \]

Substituting the frequency:

\[ \omega = 2\pi \times 50 = 100\pi \, \text{radians/second} \]

### Step 6: Calculate Time Lag
The time lag \( t \) can be calculated using the formula:

\[ t = \frac{\phi}{\omega} \]

Substituting the values:

\[ t = \frac{\frac{\pi}{6}}{100\pi} = \frac{1}{600} \, \text{seconds} \]

### Final Answer
The time lag between the maximum voltage and current is:

\[ t = \frac{1}{600} \, \text{seconds} \]

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