Let me analyze the questions in your uploaded image and solve them step by step. I’ll start with the first question:

Question 1: A Series RLC Circuit

Circuit Details:

• Resistance $R = 10 \, \Omega$
• Inductance $L = 0.18 \, \text{H}$
• Capacitance $C = 120 \, \mu\text{F}$
• Voltage $V = 240 \, \text{V}$
• Frequency $f = 50 \, \text{Hz}$

Solution:

1. Angular frequency: $\omega = 2 \pi f = 2 \pi \cdot 50 = 314.16 \, \text{rad/s}$

2. Inductive reactance: $X_L = \omega L = 314.16 \cdot 0.18 = 56.55 \, \Omega$

3. Capacitive reactance: $X_C = \frac{1}{\omega C} = \frac{1}{314.16 \cdot 120 \cdot 10^{-6}} = 26.53 \, \Omega$

4. Net reactance: $X = X_L - X_C = 56.55 - 26.53 = 30.02 \, \Omega$

5. Impedance: $Z = \sqrt{R^2 + X^2} = \sqrt{10^2 + 30.02^2} = \sqrt{100 + 900.8} = 31.62 \, \Omega$

6. Circuit current: $I = \frac{V}{Z} = \frac{240}{31.62} = 7.59 \, \text{A}$

7. Phase angle: $\theta = \tan^{-1}\left(\frac{X}{R}\right) = \tan^{-1}\left(\frac{30.02}{10}\right) = \tan^{-1}(3.002) = 71.57^\circ$

8. Power factor: $\text{Power Factor} = \cos\theta = \cos(71.57^\circ) = 0.325$

Final Answers:

• (a) Impedance $Z = 31.62 \, \Omega$
• (b) Circuit current $I = 7.59 \, \text{A}$
• (c) Phase angle $\theta = 71.57^\circ$
• (d) Power factor = 0.325

Would you like me to continue with Question 2 or any other specific part? Let me know!