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.