Impedance sounds strange for people who do not study electric circuits in advanced level. Impedance is often used in ac electric circuit analysis as well as resistance in dc electric circuit. The difference between these two is, impedance has magnitude and phase, while resistance only has magnitude.

*Make sure to read what is ac circuit first.*## Impedance and Admittance

From the previous post about sinusoidal and phasor, we knew the voltage-current relations for three passive elements of R, L, and C as(1) |

Theimpedance Zof a circuit is the ratio of the phasor voltageVto the phasor currentI, measured in ohms (Ω)

The impedance shows the opposition that the circuit exhibits to the flow of sinusoidal current. Although the impedance is the ratio of two phasors, it is not a phasor, because it does not correspond to a sinusoidally varying quantity.

The impedance of resistors, inductors, and capacitors can be readily obtained from Equation.(2). Table.1 gives a summary of their impedances.

Table.1 |

**Z**

_{L}=

*jωL*and

**Z**

_{C}=

*-j/ωC*. Consider two extreme cases of angular frequency. When

*ω*= 0 (i.e., for dc sources),

**Z**

_{L}= 0 and

**Z**

_{C}→ ∞, confirming what we already know - that the inductor acts like a short circuit, while the capacitor acts like an open circuit.

When

As a complex quantity, the impedance may be written in rectangular form as

*ω*→ ∞ (i.e., for high frequencies),**Z**_{L}→ ∞ and**Z**_{C}= 0, showing that the inductor is an open circuit, while the capacitor is a short circuit as can be seen in Figure.(1).Figure 1. Equivalent circuits at dc and high frequencies: (a) inductor, (b) capacitor |

(4) |

*R*= Re

**Z**is the

**resistance**and

*X*= Im

**Z**is the

*reactance*. The reactance X may be negative or positive. We may say that the impedance is inductive when

*X*is positive or capacitive when

*X*is negative.

Hence, impedance

**Z**=

*R + jX*is said to be

*inductive*or lagging since current lags voltage, while impedance

**Z**=

*R - jX*is

*capacitive*or leading since current leads voltage. All three impedance, resistance, and reactance are measured in ohms. The impedance may also be expressed in polar form as

TheadmittanceY 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

(9) |

As a complex quantity, we may write Y as

(10) |

*G*= Re

**Y**is called the

*conductance*and

*B*= Im

**Y**is called the

*susceptance*. Admittance, conductance, and susceptance are all expressed in the unit of siemens (or mhos). From Equations.(4) and (10),

## Impedance and Admittance Example

For better understanding let us review the example below :

**1. Find**

*v(t)*and*i(t)*in the circuit in Figure.(2)
From the voltage source 10 cos 4

*t*,*ω*= 4,
Notice that

Untuk Bahasa Indonesia baca Rumus Impedansi dan Admitansi Rangkaian AC

*i(t)*leads*v(t)*by 90^{o}as expected.Have you understood what is impedance? Don't forget to share and subscribe! Happy learning!

*Reference: Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku*Untuk Bahasa Indonesia baca Rumus Impedansi dan Admitansi Rangkaian AC

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