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Circuit Analysis III

This section delves into circuit analysis when multiple sources are present. It highlights how to apply Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) to solve for all currents and voltages in a complex circuit. Learn to identify nodes and loops, create KCL equations for each node, and KVL equations for each loop. The step-by-step process is illustrated with examples involving multiple branches and components. Gain a clear understanding of impedance and power consumption calculations in electrical engineering.

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Circuit Analysis III

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  1. Circuit Analysis III Section 06

  2. Multiple Sources • What if more than one source in the circuit? • How to solve for all currents?

  3. KVL and KCL • (nodes, loops, planner circuit, voltage drop) then what? • To solve for all currents and volts in a circuit: • KVL: Kirchhoff’s Voltage Law • the algebraic sum of voltages in a loop is zero • KCL: Kirchhoff’s Current Law • the algebraic sum of currents into a node is zero

  4. Circuit Analysis • count nodes minus one (possible ground) • mark a current for each branch • name and direction • write KCL equations for each node • count the loops • write the KVL equations for each loop • solve for all unknowns

  5. Example - - + + + + - - 1 1 2 0

  6. Example - - + + + + - - 1 0

  7. Example 8 branches  8 currents I1..I8  8 equations 4 nodes  4 eqs 4 loops  4 eqs

  8. Impedance • treat all passive components as resistors • but with complex resistances Electrical Engineering Umm Al-Qura University

  9. Impedance • What is the impedance of a 10mF capacitor when operated at 60Hz? • What is the impedance of a 2mH inductor when operated at 60Hz? Electrical Engineering Umm Al-Qura University

  10. Example Electrical Engineering Umm Al-Qura University

  11. Solution Electrical Engineering Umm Al-Qura University

  12. Simulation Solution Electrical Engineering Umm Al-Qura University

  13. Current Source • Voltage Source • Generates constant volt regardless of the load • Current Source • Generates constant current regardless of the load Electrical Engineering Umm Al-Qura University

  14. KVL & KCL + vx - Electrical Engineering Umm Al-Qura University

  15. Example Electrical Engineering Umm Al-Qura University

  16. Power • Power = rate of energy transfer • measured in Watts (W) Electrical Engineering Umm Al-Qura University

  17. Process Check • Solve the circuit shown and find the power consumption of each component Electrical Engineering Umm Al-Qura University

  18. Solution (1) Electrical Engineering Umm Al-Qura University

  19. Solution (2) Electrical Engineering Umm Al-Qura University

  20. Total Power = 0 Total Power = Zero Electrical Engineering Umm Al-Qura University

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