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To solve this problem, we can go through the required steps based on the information provided:

### Given Data:
- Voltage \( V = 230 \, \text{V} \)
- Current \( I = 12 \, \text{A} \)
- Power \( P = 2208 \, \text{W} \)

### Calculations:

1. **Power Factor (\( \cos \varphi \))**:
   - The power factor \( \cos \varphi \) can be calculated using the formula:
     \[
     \cos \varphi = \frac{P}{V \cdot I}
     \]
   - Substituting the values:
     \[
     \cos \varphi = \frac{2208}{230 \times 12} \approx 0.8
     \]

2. **Reactive Power (VAr)**:
   - The reactive power \( Q \) (in VAr) can be calculated using:
     \[
     Q = V \cdot I \cdot \sin \varphi
     \]
   - First, calculate \( \sin \varphi \) using \( \cos \varphi \):
     \[
     \sin \varphi = \sqrt{1 - (\cos \varphi)^2} = \sqrt{1 - 0.8^2} \approx 0.6
     \]
   - Then, calculate \( Q \):
     \[
     Q = 230 \times 12 \times 0.6 \approx 1656 \, \text{VAr} \, (\approx 1.65 \, \text{kVAr})
     \]

3. **Impedance \( Z \) (magnitude and phase)**:
   - The impedance \( Z \) magnitude is given by:
     \[
     Z = \frac{V}{I} = \frac{230}{12} \approx 19.17 \, \Omega
     \]
   - The phase angle \( \theta \) is the arccosine of the power factor:
     \[
     \theta = \cos^{-1}(0.8) \approx 36.87^\circ
     \]

4. **Resistance \( R \) and Inductive Reactance \( X_L \)**:
   - The resistance \( R \) is calculated as:
     \[
     R = Z \cdot \cos \theta = 19.17 \times 0.8 \approx 15.3 \, \Omega
     \]
   - The inductive reactance \( X_L \) is:
     \[
     X_L = Z \cdot \sin \theta = 19.17 \times 0.6 \approx 11.5 \, \Omega
     \]

### Summary of Results:
- **a) Power Factor (\( \cos \varphi \))**: \( 0.8 \)
- **a) Reactive Power (VAr)**: \( 1.65 \, \text{kVAr} \)
- **b) Impedance \( Z \)**: \( 19.17 \, \Omega \) at \( 36.87^\circ \)
- **c) Resistance \( R \)**: \( 15.3 \, \Omega \)
- **c) Inductive Reactance \( X_L \)**: \( 11.5 \, \Omega \)

Would you like to delve further into any part of this solution, or have any other questions?

### Follow-up Questions:
1. How would changes in the current affect the reactive power?
2. What is the significance of a power factor of 0.8 in practical scenarios?
3. How does inductive reactance \( X_L \) affect the overall circuit behavior?
4. Why is the impedance phase angle relevant in AC circuits?
5. How could this analysis change if the motor was connected to a different voltage?

### Tip:
In AC circuits, always remember that reactive power (measured in VAr) doesn't contribute to the actual work done but impacts the phase angle and overall power efficiency.

Un motor M es conectado a una red de distribución monofásica alterna. A fin de determinar su funcionamiento, se le conecta un amperímetro, voltímetro, y vatímetro. Si estos instrumentos tienen las lecturas indicadas en la figura, determinar: a) El cosφ y los VAr consumidos por el motor. b) Impedancia en módulo y fase. c) Resistencia R y reactancia inductiva del circuito X_L equivalente del motor, asumiendo conexión serie entre ambos.

This guide explains how to determine the power factor, reactive power, impedance, resistance, and inductive reactance for an AC motor connected to a single-phase circuit. Given voltage, current, and power readings, the solution includes key formulas and step-by-step calculations for advanced electrical engineering students.

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