**Generalized Ohm's Law**

The Ohm's law in DC circuit composed of resistors only can be
generalized to describe the relationship between the sinusoidal voltage
and current associated with a component, a capacitor , an inductor ,
or a resistor . The *impedance* of the component is defined as the
ratio of the AC voltage and current associated with the component both
represented as complex variables or phasors:

The impedance is in general complex and its magnitude is the ratio of the magnitudes of the voltage and the current, and its phase is the phase difference between the voltage and the current:

As phasor representation of a sinusoidal voltage or a current of frequency
is actually the only Fourier coinfficient in the frequency
domain, the impedance can be considered as the *frequency response function*
of the circuit component when the current through it and the voltage across it,
both represented as phasors, are considered as the input and output of the
component, respectively. As there is only one frequency in the signal, it
does not need to be represented.

**Impedance of Basic Components**

The impedance of a specific component can be obtained according to the physics of the component.

**Resistor:**

As a resistor introduces no phase shift between the voltage and current, its impedance, same as resistance, is real:

**Capacitor:**

The phase shift introduced by a capacitor is , i.e., the voltage lags behind the current by .**Inductor:**

The phase shift introduced by a inductor is , i.e., the voltage leads the current by .

- When , and the capacitor has zero conductivity due to the insulation between its two plates (open circuit), and as there is no flux change in the inductor and the resistance of the coil is ideally zero.
- When , and the capacitor becomes highly conductive, and as the self-induced voltage in the coil always acts against any change in the input (Lenz's Law).

**Impedance and Admittance**

**Impedance**As a complex variable, the impedance can be written as:

- The real part of impedance is called
**resistance**. - The imaginary part of impedance is called
**reactance**.

The magnitude and phase angle of are:

The impedances associated with and are both purely imaginary, i.e., they are both reactance, indicating these components are reactive and consume no energy.- The real part of impedance is called
**Admittance**The reciprocal of the impedance is called

**admittance**:

- The real part of admittance is called
**conductance**:

- The imaginary part of admittance is called
**susceptance**:

The magnitude and phase of complex admittance are

- The real part of admittance is called

Impedance and admittance are both complex variables. The real parts and are always positive, but the imaginary parts and can be either positive or negative. Therefore and can only be in the 1st or the 4th quadrants of the complex plane.

In particular, the admittances of the three types of elements R, L
and C are

Ohm's law can also be expressed in terms of admittance as well as impedance:

Sometimes it is more convenient in circuit analysis to use admittance instead of impedance.

- Components parallel:

- Components in series: