Electrical Engineering 1 Course Notes 2024-2025 PDF

Electrical Engineering 1 – EE1 Fundamentals of Electrical Engineering 1 – FEE1 Course notes Assoc. Prof. PhD. Eng. Mihai Iulian REBICAN 2024 - 2025  Electric circuits in variable state EE1+FEE1 – cour...

Electrical Engineering 1 – EE1 Fundamentals of Electrical Engineering 1 – FEE1 Course notes Assoc. Prof. PhD. Eng. Mihai Iulian REBICAN 2024 - 2025  Electric circuits in variable state EE1+FEE1 – course 8 Variable state: current through an element and voltage along an element are not constant in time, they can have any variation in time (sinusoidal, exponential, step variations and so on). First Kirchhoff’s theorem: Second Kirchhoff’s theorem: Power corresponding to an one-port element:  Ideal passive circuit elements Resistor Capacitor Capacitor is an one-port element for which current through the element depends on velocity (derivate) of voltage along the element. Symbol: Parameter of a capacitor is capacitance, C, given in farads: C [F]. Equation: - for receiver convention: - for generator convention: Obs.: Capacitor is a symmetric element (it does not matter how it is connected in circuit). Voltage on capacitor is: where t0 is the initial time, u(t0) is the voltage at initial time (initial voltage or initial condition of the capacitor). Obs.: Voltage along a capacitor has a continuous variation in time (at initial time, voltage is the same, u(t0)). But the current does not have a continuous variation in time (a jump of current at initial time). Particular cases: a) if C=0, then i(t)=0 (any u): open-circuit b) If u(t)=U=constant in time (DC circuit), then i(t)=0 (any u): open-circuit Obs.: In DC circuits, the capacitor behaves as an open-circuit. Energetic characterization (transferred power): Electric energy stored by capacitor: Power is transferred from circuit to element. The capacitor is a passive element, a reactive element, which store electric energy! Inductor Inductor is an one-port element for which voltage along the element depends on velocity (derivate) of current through the element. Symbol: Parameter of an inductor is inductance, L, given in henrys: L [H]. Equation: - for receiver convention: - for generator convention: Obs.: Inductor is a symmetric element (it does not matter how it is connected in circuit). Current through inductor is: where t0 is the initial time, i(t0) is the current at initial time (initial current or initial condition of the inductor). Obs.: Current through an inductor has a continuous variation in time (at initial time, current is the same, i(t0)). But the voltage does not have a continuous variation in time (a jump of voltage at initial time). Particular cases: a) if L=0, then u(t)=0 (any i): short-circuit b) If i(t)=I=constant in time (DC circuit), then u(t)=0 (any i): short-circuit Obs.: In DC circuits, the inductor behaves as a short-circuit. Energetic characterization (transferred power): Magnetic energy stored by inductor: Power is transferred from circuit to element. The inductor is a passive element, a reactive element, which store magnetic energy! Coupled inductors (inductors with mutual coupling) Coupled inductors represent a multi-ports element. So, two coupled inductors mean a two-ports elements. There is a magnetic coupling between two inductors, so the inductors are not independently. The voltage along one inductor depends on velocity (derivate) of current through the inductor and velocity (derivate) of current through the other inductor from the magnetic coupling. Obs.: Magnetic coupling is represented by stars (polarized terminals). Obs.: For both inductors, the voltage and current are oriented according to receiver convention. L1=L11 is the self inductance of the first inductor L2=L22 is the self inductance of the second inductor M=L12=L21 is the mutual inductance of the two inductors Obs.: L1>0, L2>0, M>0 or M0)!  Ideal active circuit elements Ideal voltage source Ideal current source Real branches Real branches with magnetic coupling inductors