A resistance of `300Omega` and an inductance of `1/(pi)` henry are connected in series to an `AC` voltage of `20 "volts"` and `200Hz` frequency. The phase angle between the voltage and current is

Options

A. `tan^(-1). 4/3`
B. `tan^(-1). 3/4`
C. `tan^(-1). 3/2`
D. `tan^(-1). 2/5`

Answer

To find the phase angle between the voltage and current in an AC circuit with a resistance and an inductor in series, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Resistance (R) = 300 Ω
- Inductance (L) = \( \frac{1}{\pi} \) H
- Frequency (f) = 200 Hz
- AC Voltage (V) = 20 V (RMS value)

2. **Calculate the Angular Frequency (ω):**
- The angular frequency (ω) is related to the frequency (f) by the formula:
\[ \omega = 2\pi f \]
- Substituting the value of f:
\[ \omega = 2\pi \times 200 = 400\pi \, \text{rad/s} \]

3. **Calculate the Inductive Reactance (X_L):**
- The inductive reactance (X_L) is given by:
\[ X_L = \omega L \]
- Substituting the values of ω and L:
\[ X_L = (400\pi) \times \left(\frac{1}{\pi}\right) = 400 \, \Omega \]

4. **Calculate the Phase Angle (φ):**
- The phase angle (φ) can be found using the formula:
\[ \tan \phi = \frac{X_L}{R} \]
- Substituting the values of X_L and R:
\[ \tan \phi = \frac{400}{300} = \frac{4}{3} \]

5. **Find the Phase Angle (φ):**
- To find φ, take the arctangent (inverse tangent) of \( \frac{4}{3} \):
\[ \phi = \tan^{-1}\left(\frac{4}{3}\right) \]

### Final Answer:
The phase angle between the voltage and current is:
\[ \phi = \tan^{-1}\left(\frac{4}{3}\right) \]