A coil having an inductance of `1//pi` henry is connected in series with a resistance of `300 Omega`. If 20 volt from a 200 cycle source are impressed across the combination, the value of the phase angle between the voltage and the current is :

Options

A. 5/4.
B. 4/5.
C. 3/4.
D. 4/3.

Explanation

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

### Step 1: Identify the given values
- Inductance \( L = \frac{1}{\pi} \) henry
- Resistance \( R = 300 \, \Omega \)
- Frequency \( f = 200 \, \text{Hz} \)
- RMS Voltage \( V = 20 \, \text{V} \)

### Step 2: Calculate the inductive reactance \( X_L \)
The inductive reactance \( X_L \) is given by the formula:
\[ X_L = 2\pi f L \]
Substituting the values:
\[ X_L = 2\pi \times 200 \times \frac{1}{\pi} \]
The \( \pi \) cancels out:
\[ X_L = 2 \times 200 = 400 \, \Omega \]

### Step 3: Use the phase angle formula
In an LR circuit, the phase angle \( \phi \) between the voltage and the current can be calculated using the formula:
\[ \tan \phi = \frac{X_L}{R} \]
Substituting the values of \( X_L \) and \( R \):
\[ \tan \phi = \frac{400}{300} \]
Simplifying this gives:
\[ \tan \phi = \frac{4}{3} \]

### Step 4: Calculate the phase angle \( \phi \)
To find the phase angle \( \phi \), we take the arctangent:
\[ \phi = \tan^{-1}\left(\frac{4}{3}\right) \]

### Step 5: Conclusion
The value of the phase angle \( \phi \) can be approximated using a calculator:
\[ \phi \approx 53.13^\circ \]

Thus, the phase angle between the voltage and the current is approximately \( 53.13^\circ \).

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