2nd Week: "Phasor in Circuit Elements, Impedance & Admittance"

"Phasor Relationship for Circuit Elements"

Now that we know how to represent a voltage or current in the phasor or frequency domain, one may legitimately ask how we apply this to circuits involving the passive elements R, L, and C. What we need to do is to transform the voltage-current relationship from the time domain to the frequency domain for each element. Again, we will assume the passive sign convention.


We begin with the resistor. If the current through a resistor R is i = Im cos(ωt + φ), the voltage across it is given by Ohm’s law as

v = iR = RIm cos(ωt + φ)

Table 9.2 summarizes the time-domain and phasor-domain representations of the circuit elements.

"Impedance & Admittance"

In the preceding section, we obtained the voltage-current relations for the three passive elements as,

V = RI, V = jωLI, V =I/jωC

These equations may be written in terms of the ratio of the phasor voltage to the phasor current as,

V/I = R,  V/I = jωL,  V/I = 1/jωC

From these three expressions, we obtain Ohm’s law in phasor form for any type of element as

Z = V/I    or   V = ZI

The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in ohms.

The admittance Y is the reciprocal of impedance, measured in siemens (S).


The admittance Y of an element (or a circuit) is the ratio of the phasor current through it to the phasor voltage across it, or

Y   =   1/Z   =   I/V

Reflection:

• I learned that the impedance is equal to voltage over current just like the Ohm's Law.
• The equivalent impedance of a capacitor is a negative value.
• The admittance is the reciprocal of impedance.
• Time domain is independent to time while phasor domain is dependent.

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GOD Bless! :)

By:

AYALA, ARNY  S.   BSECE -3

ECE 321

Professor:

ENGR. JAY S. VILLAN, MEP - EE