A coil of resistance `300 Omega` and inductance 1.0 henry is connected across an voltages source of frequency `300//2pi Hz`. The phase difference between the voltage and current in the circuit is

Options

A. `(pi)/(2)`
B. `(pi)/(4)`
C. `(pi)/(3)`
D. `(pi)/(6)`

Explanation

To find the phase difference between the voltage and current in an RL circuit, we can follow these steps:

### Step 1: Identify the given values
- Resistance \( R = 300 \, \Omega \)
- Inductance \( L = 1.0 \, \text{H} \)
- Frequency \( f = \frac{300}{2\pi} \, \text{Hz} \)

### Step 2: Calculate the angular frequency \( \omega \)
The angular frequency \( \omega \) is given by the formula:
\[ \omega = 2\pi f \]
Substituting the value of \( f \):
\[ \omega = 2\pi \left(\frac{300}{2\pi}\right) = 300 \, \text{rad/s} \]

### Step 3: Calculate the inductive reactance \( X_L \)
The inductive reactance \( X_L \) is calculated using the formula:
\[ X_L = \omega L \]
Substituting the values of \( \omega \) and \( L \):
\[ X_L = 300 \times 1 = 300 \, \Omega \]

### Step 4: Calculate the phase difference \( \phi \)
The phase difference \( \phi \) in an RL circuit is given by:
\[ \tan \phi = \frac{X_L}{R} \]
Substituting the values of \( X_L \) and \( R \):
\[ \tan \phi = \frac{300}{300} = 1 \]

### Step 5: Find \( \phi \)
To find \( \phi \), we take the arctangent:
\[ \phi = \tan^{-1}(1) = \frac{\pi}{4} \, \text{radians} \]

### Conclusion
The phase difference between the voltage and current in the circuit is:
\[ \phi = \frac{\pi}{4} \, \text{radians} \]

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