Final answer:
To analyze AC circuits, we use phasor diagrams to illustrate the phase relationships between current and voltage. We calculate the equivalent emf by trigonometrically adding the phasor of the resistor to the net voltage phasors of the capacitor and inductor, considering the phase differences.
Step-by-step explanation:
Phasor Diagrams in AC Circuits Analysis:
To find IΕ, Iℓ, Vs, XΕ, C, and Zeq and create a phasor diagram, we follow a systematic approach. Phasor diagrams are graphical illustrations used to analyze the relationships between currents and voltages in AC circuits. Starting with the phasor for the resistor (UR(t)), which is in phase with the current (i(t)), we can use trigonometry to add phasors for the capacitor (vc(t)) and the inductor (UL(t)). In the case of a capacitor, the current phasor leads the voltage phasor by π/2 rad, while for an inductor, the voltage phasor leads the current phasor by π/2 rad. Using these relationships and following the mnemonic device 'ELI the ICE man', we can calculate any unknown values and draw the complete phasor diagram.
For analyzing an R, L, C series circuit, add the phasors for UR(t), UL(t), and vc(t) vectorially. The result is the equivalent phasor, which represents the overall emf of the circuit. The projection of this phasor onto the vertical axis gives the instantaneous value of the emf.