A `9//100 (pi)` inductor and a `12 Omega` resistanace are connected in series to a 225 V, 50 Hz ac source. Calculate the current in the circuit and the phase angle between the current and the source voltage.

Explanation

To solve the problem, we need to calculate the current in the circuit and the phase angle between the current and the source voltage when a 9/100 π H inductor and a 12 Ω resistor are connected in series to a 225 V, 50 Hz AC source.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Inductance, \( L = \frac{9}{100} \pi \) H
- Resistance, \( R = 12 \, \Omega \)
- Voltage, \( V = 225 \, V \)
- Frequency, \( f = 50 \, Hz \)

2. **Calculate Angular Frequency (ω):**
\[ \omega = 2\pi f = 2\pi \times 50 = 100\pi \, \text{rad/s} \]

3. **Calculate Inductive Reactance (XL):**
\[ X_L = L \cdot \omega = \left(\frac{9}{100} \pi\right) \cdot (100\pi) = 9 \, \Omega \]

4. **Calculate Impedance (Z):**
The impedance \( Z \) in a series circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values:
\[ Z = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 \, \Omega \]

5. **Calculate Current (I):**
Using Ohm's Law for AC circuits, the current \( I \) can be calculated as:
\[ I = \frac{V}{Z} = \frac{225}{15} = 15 \, A \]

6. **Calculate Phase Angle (φ):**
The phase angle \( \phi \) between the current and the voltage is given by:
\[ \tan \phi = \frac{X_L}{R} \]
Substituting the values:
\[ \tan \phi = \frac{9}{12} = \frac{3}{4} \]
Now, calculate \( \phi \):
\[ \phi = \tan^{-1}\left(\frac{3}{4}\right) \approx 36.86^\circ \]

### Final Answers:
- The current in the circuit is \( 15 \, A \).
- The phase angle between the current and the source voltage is approximately \( 36.86^\circ \).