Answer the following points in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, properties of phasors, among others). a) Suppose that between the two terminals of an element there is a voltage v (t) and that a current i (t) enters through the terminal marked with a positive sign. Show that if v (t) and i (t) are sinusoidal and are out of phase by an angle ϕ, then the active power P that is consumed by said element is proportional to cos ϕ b) How much is P for a pure inductor and how much for a pure capacitor? Does this make physical sense? c) When specifying the power factor seen between two terminals, why is it necessary to indicate whether it is lagging or leading?
Answer the following points in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, properties of phasors, among others).
a) Suppose that between the two terminals of an element there is a voltage v (t) and that a current i (t) enters through the terminal marked with a positive sign. Show that if v (t) and i (t) are sinusoidal and are out of phase by an angle ϕ, then the active power P that is consumed by said element is proportional to cos ϕ
b) How much is P for a pure inductor and how much for a pure capacitor? Does this make physical sense?
c) When specifying the power factor seen between two terminals, why is it necessary to indicate whether it is lagging or leading?
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