Alternating Current (AC) is the form of electricity most often delivered to homes and businesses, characterized by a voltage and current that periodically reverse direction and continuously change magnitude. While Direct Current (DC) faces straightforward opposition to flow, the constantly changing nature of AC introduces a more complicated challenge to the movement of electrons. In AC circuits, the opposition to current flow is not solely defined by simple resistance but by a more encompassing property known as impedance.
Defining Impedance and Resistance
Impedance (\(Z\)) is the total opposition a circuit presents to the flow of alternating current, measured in Ohms (\(\Omega\)). This concept extends electrical resistance (\(R\)), which is the opposition found in both AC and DC circuits. Resistance is caused by electron collisions within a conductor, converting electrical energy permanently into heat. For a pure resistor, the value of \(R\) remains the same regardless of the AC signal frequency.
Impedance includes resistance along with another form of opposition involving energy storage and return. While resistance only accounts for energy consumed, impedance accounts for all opposition, including power consumption and temporary storage. Consequently, the value of impedance is dependent on the frequency of the alternating current. A circuit’s impedance may change significantly if the frequency of the power source is altered, unlike pure resistance.
The Two Forms of Reactance
The opposition component within impedance that is not resistance is called reactance (\(X\)). Reactance is the manifestation of electric and magnetic fields that store energy during one part of the AC cycle and release it back in the next. This energy storage capability means that, unlike resistance, reactance does not permanently convert electrical energy into heat. Reactance is categorized into two forms, each caused by a different type of circuit component.
Inductive Reactance
Inductive reactance (\(X_L\)) is produced by inductors, typically coils of wire. An inductor opposes changes in current by generating a magnetic field that creates a voltage pushing back against the source (back EMF). This opposition is proportional to the rate of change of the current. As the AC frequency increases, the inductive reactance also increases. Inductive reactance causes the voltage waveform to peak before the current waveform, meaning the voltage “leads” the current.
Capacitive Reactance
Capacitive reactance (\(X_C\)) is created by capacitors, which store electrical energy in an electric field. A capacitor opposes changes in voltage by accumulating charge on its plates. Unlike inductive reactance, capacitive reactance is inversely proportional to the AC frequency. As the frequency increases, the capacitive reactance decreases, allowing current to flow more easily. Capacitive reactance causes the current waveform to peak before the voltage waveform, meaning the current “leads” the voltage.
These two forms of reactance, \(X_L\) and \(X_C\), have opposite effects on the timing relationship between voltage and current. In any AC circuit, the total reactance is the net result of the inductive and capacitive effects.
Combining Resistance and Reactance
Total impedance (\(Z\)) is the combination of the circuit’s resistance (\(R\)) and its net reactance (\(X\)). Because resistance dissipates energy and reactance stores energy, they do not oppose current flow in the same manner. This functional difference causes the current through resistive components to be synchronized with the voltage, while the current through reactive components is out of sync by a quarter cycle. Specifically, the resistive and reactive forces are 90 degrees out of phase.
Due to this phase difference, resistance and reactance cannot be simply added using standard arithmetic. Instead, total impedance must be calculated using vector mathematics, which accounts for the phase difference. This relationship is often visualized using the “Impedance Triangle,” where resistance forms one side, reactance forms a perpendicular side, and impedance is the hypotenuse.
The result of this combination is the magnitude of the total opposition and the phase angle (\(\phi\)). The phase angle describes the time difference between the overall voltage and current waveforms. A positive phase angle indicates the circuit is predominantly inductive (voltage leading current). Conversely, a negative phase angle shows the circuit is predominantly capacitive (current leading current). This phase angle dictates how efficiently power is transferred.
Why Impedance Matters in AC Systems
Understanding impedance is fundamental to the design and operation of nearly all alternating current systems. One important application is impedance matching, which ensures a source’s output impedance aligns with a load’s input impedance. In audio systems, matching an amplifier’s output impedance to a loudspeaker’s impedance achieves maximum power transfer. Mismatched impedance leads to reduced power output and signal reflection, a problem in radio frequency (RF) systems that results in poor signal quality.
Impedance characteristics are also utilized in the creation of filters. Since inductive and capacitive reactances change with frequency, components can be arranged to selectively block or pass certain frequencies. For example, a high-pass filter uses a capacitor’s decreasing impedance at higher frequencies to allow those signals to pass while blocking lower-frequency signals. This principle is used in devices ranging from radio receivers, which tune into a single frequency, to power supply systems, where unwanted high-frequency noise must be filtered out.