University Circuit Theory Problem Solver

I have a university-level circuit theory question that requires solving for the value of a capacitor using five different theorems. The circuit needs to be analyzed using the following theorems:

- Mesh Analysis
- Nodal Analysis
- Superposition Theorem
- Thevenin’s Theorem
- Norton’s Theorem

I need detailed calculations and explanations for each solution using these methods. Please ensure accuracy and clarity in the calculations, as this is for an academic requirement.

Please provide the final solution in a PDF document. Please complete the project within a week. The circuit being analyzed is an AC circuit. Provide step-by-step explanations of each theorem in the PDF document. Specific components and values for the circuit are provided.