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AC Circuit Analysis Techniques

Apr 24, 2025

AC Circuit Analysis Lecture

Overview

  • Goal: Determine voltage and current across every component in an AC circuit with both parallel and series components.
  • Strategy: Combine components to form an equivalent circuit, calculate voltage and current, expand back to original circuit.

Steps for Circuit Analysis

  1. Calculate Impedances

    • Determine the impedance for each component: inductors and capacitors.
    • Use the formulas:
      • Capacitor: ( X_C = \frac{1}{2\pi fC} )
      • Inductor: ( X_L = 2\pi fL )
    • Frequency used: 60 Hz

  2. Create Equivalent Circuits

    • First Equivalent Circuit: Combine inductor and capacitor.
      • Result: ( Z_{L1} + Z_2 = j 245.04 \Omega - j 1768.4 \Omega )
      • Conclusion: Acts like a capacitor with a phase angle of -90°.
    • Second Equivalent Circuit: Combine resistor ( R_2 ) with series of inductor ( L1 ) and capacitor ( C2 ).
    • Third Equivalent Circuit: Add capacitor ( C1 ) to the combined impedance.

  3. Calculate Total Impedance and Current

    • Convert values to polar coordinates to find total impedance.
    • Calculate total current ( I_T ) using total impedance.

  4. Backward Calculation of Voltages and Currents

    • Third to Second Equivalent Circuit: Calculate voltage across ( C1 ) and series components.
    • Second to First Equivalent Circuit: Voltage across ( R1 ) in parallel with ( L1 + C2 ).
    • Calculate Component Currents: For each component using voltages and impedances.
    • Final Calculations: Voltage across ( L1 ) and ( C2 ) using current and impedances._

Final Results

  • Table: Displays calculated voltages, currents, and impedances for each component.
    • Components include: ( C1, L1, C2, R1 )
    • Total values are also presented.

Additional Resources

  • Example problem and calculations from a free open-source textbook.
  • Link to the problem and textbook provided in the video description.
  • Topics covered in the resource: AC circuits, DC circuits, communication systems, electronics.

Conclusion

  • The lecture provides a detailed analysis of mixed AC circuits combining series and parallel components.
  • Thank you for attending; more topics on electronic and digital circuits will be covered in future lectures.

Note: For detailed calculations and steps, refer to the provided video or supporting materials in the description.

Full transcript