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ADV/TEC 2 : Introducing AC Circuits

ADV/TEC 2 : Introducing AC Circuits. Introductory mini-lecture. AC Voltage. Voltage varies with time: v(t) = V 0 cos( ω t ) V 0 is the voltage amplitude v(t) is the instantaneous voltage ω =2 π f is the angular frequency (in radians/s). Complex Notation.

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ADV/TEC 2 : Introducing AC Circuits

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  1. ADV/TEC 2: Introducing AC Circuits Introductory mini-lecture

  2. AC Voltage • Voltage varies with time: v(t) = V0cos(ωt) • V0is the voltage amplitude • v(t) is the instantaneous voltage • ω=2πf is the angular frequency (in radians/s)

  3. Complex Notation • We define a complex voltage v =V0ejωt = V0cos(ωt) + jV0sin(ωt) where (we use j because i is used for current) • Complex notation is a convenient mathematical model for vector quantities • The instantaneous voltage is the real part of the complex voltage

  4. Resistors in AC Circuits • Ohm’s Law still holds for resistors in AC circuits • If the supplied voltage to a resistor is v =V0ejωt, then the current through the resistor is i= v/R = (V0/R)ejωt = I0ejωt

  5. Internal Resistance • All real signal sources can be represented by an ideal source in series with a resistor (internal resistance). This combination is called the Théveninequivalent circuit.

  6. Phasor Diagrams • We represent complex numbers graphically by Argand diagrams: x-axis is the real part, y-axis is the imaginary part • Complex voltage v =V0ejωt is then a vector that rotates counter-clockwise with time • Instantaneous voltage is its projection onto the x-axis

  7. Phasor Diagrams

  8. Phasor Diagrams Yellow= voltage Green= current Note that current and voltage are in phase

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