ECE 3301 General Electrical Engineering Presentation 35 Circuit Laws and Phasors

Kirchhoff’s Voltage Law Consider a circuit with circuit elements and voltages as shown below:

Kirchhoff’s Voltage Law Assume the network is excited by independent sinusoidal sources at radian frequency w.

Kirchhoff’s Voltage Law The voltage across any circuit element will be a sinusoid at the frequency w with some amplitude and phase angle.

Kirchhoff’s Voltage Law Kirchhoff’s Voltage Law must be true around any closed loop.

Kirchhoff’s Voltage Law The sum of Phasor Voltages around any closed loop is equal to zero.

Kirchhoff’s Current Law Consider a circuit with circuit elements and currents as shown below:

Kirchhoff’s Current Law Assume the network is excited by independent sinusoidal sources at radian frequency w.

Kirchhoff’s Current Law The current through any circuit element will be a sinusoid at the frequency w with some amplitude and phase angle.

Kirchhoff’s Current Law Kirchhoff’s Current Law must be true at any node.

Kirchhoff’s Current Law The sum of Phasor Currents into any node is equal to zero.

Impedances in Series VS = V1 + V2 + … + Vn VS = I Z1 + I Z2 + … + I Zn VS = I (Z1 + Z2 + … + Zn ) VS = I Zeq Zeq = Z1 + Z2 + … + Zn

Impedances in Parallel

Impedances in Parallel

Impedances in Parallel

DC Circuits and AC Circuits All of the techniques and theorems from DC Resistive Circuits also apply to AC Circuits, now using Complex Numbers. Voltage Divider Equation Current Divider Equation Source Transformations Node Voltage Analysis Mesh Current Analysis Matrix Equations and Cramer’s Rule Superposition Theorem Thevenin Equivalent Circuit Norton Equivalent Circuit Maximum Power Transfer (More on this later) Operational Amplifier Circuits