a) Suppose that between the two terminals of an element there is a voltage v (t) and that through the terminal marked with a positive sign a current i (t). Show that if v (t) and i (t) are sinusoidal and are out of phase an angle θ, then the active power P which is consumed by this element is proportional to cosθ. b) How much is P for a pure inductor and how much for a capacitor pure? Does this make physical sense? c) When the power factor seen between two terminals is specified, Why is it necessary to indicate whether it is late or early?
Please answer the following points in detail and rigorously. Instead of
resort 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 through the terminal marked with a positive sign a current i (t). Show that if v (t) and i (t) are sinusoidal and are out of phase an angle θ, then the active power P which is consumed by this element is proportional to cosθ.
b) How much is P for a pure inductor and how much for a capacitor pure? Does this make physical sense?
c) When the power factor seen between two terminals is specified, Why is it necessary to indicate whether it is late or early?
d) Show that the complex power consumed by two elements in parallel is the sum of the individual complex powers. After, repeat the procedure but for two elements in series.
e) What meaning would you give to the P consumed by an element? Which to Q?
f) Suppose you know P and Q for a two-terminal element. What is the power factor of this element? When would i be in early and when behind?
g) Suppose you know the equivalent resistance R and the reactance X equivalent of a two-terminal passive network. What is the factor power of red bliss? When would I be in advance and when in backwardness?
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