The image shows an RLC Parallel Circuit task where we need to solve for various parameters of the circuit based on the provided schematic and measured data. Here's a breakdown of the task and how to approach it:

Given Data:

• Supply Voltage (Vs): 12V
• Resistor (R): $33 \, \Omega$
• Inductor (L): $91 \, \text{mH}$
• Capacitor (C): $220 \, \mu \text{F}$

Task Breakdown:

1. Construct the RLC Series Circuit and Measure:

   • (A) Supply Voltage: Given as 12V.
   • (B) Branch current magnitude and angle for the resistive component: To calculate this, use Ohm’s Law $I_R = \frac{V}{R}$. For phase angle, since it's purely resistive, the angle $\theta_R = 0^\circ$.
   • (C) Branch current magnitude and angle for the inductive component: The inductive reactance is $X_L = 2\pi fL$. Then, the current $I_L = \frac{V}{X_L}$. The phase angle for an inductor is $\theta_L = +90^\circ$ (current lags voltage).
   • (D) Branch current magnitude and angle for the capacitive component: The capacitive reactance is $X_C = \frac{1}{2\pi fC}$. The current $I_C = \frac{V}{X_C}$. The phase angle for a capacitor is $\theta_C = -90^\circ$ (current leads voltage).

2. Using Measured Values:

   • (E) Draw and label the RLC series phasor diagram: This would involve plotting the vectors for $I_R$, $I_L$, and $I_C$ with appropriate phase angles.
   • (F) Determine supply current magnitude via phasor diagram: Use vector addition to sum the phasor currents $I_R$, $I_L$, and $I_C$.
   • (G) Determine the circuit phase angle via phasor diagram: Calculate the overall phase angle $\theta$ using the phasor sum of the currents.
   • (H) Determine the circuit phase angle via phasor diagram: Repeated to ensure clarity in the calculation process.
   • (I) Determine the relationship between supply voltage and circuit current: This involves understanding whether the circuit is capacitive or inductive based on the resultant phase angle.

Formulas:

• Resistive Current: $I_R = \frac{V_s}{R}$
• Inductive Reactance: $X_L = 2\pi f L$
• Capacitive Reactance: $X_C = \frac{1}{2\pi f C}$
• Inductive Current: $I_L = \frac{V_s}{X_L}$
• Capacitive Current: $I_C = \frac{V_s}{X_C}$

Would you like to continue with a more detailed step-by-step calculation of the current, phase angles, and phasor diagram? Let me know if you need help with any particular calculation or part of the task.

Additional Related Questions:

1. How do we calculate the total impedance of a parallel RLC circuit?
2. What is the resonance frequency of this RLC circuit?
3. How does the phase angle change as frequency varies in an RLC circuit?
4. How can we experimentally verify the calculated phase angles?
5. What are the effects of changing the capacitor’s value on the circuit’s behavior?

Tip: Always start with calculating individual branch currents and their phase angles, then combine them using phasor algebra to find the total current and phase angle.