5.2Resistance, Reactance, and Impedance

Resistance (R) is the dissipative opposition to an electric current, analogous to friction encountered by a moving object. In any example of electrical resistance, the electrical energy is converted into some other form of energy that cannot (or does not) return back to the circuit. Resistance may take the form of an actual resistor, in which case the electrical energy is converted into heat. Resistance may also take the form of an electric motor, an electric light, or an electrochemical cell where the electrical energy is converted into mechanical work, photons, or enables an endothermic chemical reaction, respectively.

Reactance (X) is the opposition to an electric current resulting from energy storage and release between certain components and the rest of the circuit, analogous to inertia of a moving object. Capacitors and inductors are classic examples of “reactive” electrical components, behaving either as electrical loads or as electrical sources depending on whether the applied electrical signal is increasing or decreasing in intensity at that instant in time. When a purely reactive component is subjected to a sinusoidal signal, it will spend exactly half the time behaving as a load (absorbing energy from the circuit) and half the time behaving as a source (returning energy to the circuit). Thus, a purely reactive component neither contributes nor dissipates any net energy in the circuit, but merely exchanges2 energy back and forth. Even though the fundamental mechanism of reactance (energy storage and release) is di erent from the fundamental mechanism of resistance (energy conversion and dissipation), reactance and resistance are both expressed in the same unit of measurement: the ohm (Ω).

Impedance (Z) is the combined total opposition to an electric current, usually some combination of electrical resistance (energy dissipation) and electrical reactance (energy storage and release). It is also expressed in the unit of the ohm. In order to represent how much of a particular impedance is due to resistance and how much is due to reactance, the value of an impedance may be expressed as a complex number with a “real” part (representing resistance) and an “imaginary” part (representing reactance). This concept will be explored in much more detail later in this chapter.

The amount of electrical reactance o ered by a capacitor or an inductor depends on the frequency of the applied signal. The faster the rate at which an AC signal oscillates back and forth, the more a reactive component tends to react to that signal. The formulae for capacitive reactance (XC ) and inductive reactance (XL) are as follows:

Just as conductance (G) is the reciprocal of resistance (1/R), a quantity called susceptance (B) is the reciprocal of reactance (1/X). Susceptance is useful when analyzing parallel-connected reactive components while reactance is useful for analyzing series-connected reactive components, in much the same way that conductance and resistance are useful when analyzing parallel-connected and series-connected resistors, respectively.

Impedance (Z) also has a reciprocal counterpart known as admittance (Y ).

2Charles Proteus Steinmetz, in his book Theoretical Elements of Electrical Engineering, refers to the voltage and current values of a reactive component being “wattless” in honor of the fact that they transfer zero net power to or from the circuit (page 41). The voltage and current values of resistive components, by contrast, constitute real power dissipated in the circuit.