Electrical impedance

Electricity moves through wires.

Sometimes, parts in a wire slow it down. This is like a tiny brake for electricity.

Some electricity moves in waves. This is called alternating current. In these waves, parts can push back. This push back is called impedance.

Impedance depends on how fast the waves move. It can change with the speed of the wave. It also tells us how the waves line up. This helps us study how power works. It is a very useful tool for engineers.

Electricity moves in different ways. Some flows in one direction. This is called direct current. Other electricity moves in waves. We call these waves alternating current, or AC.

In AC circuits, parts can push back against the flow. This push back is called impedance.

Impedance is more than just resistance. Resistance only slows things down. Impedance also includes reactance. Reactance comes from two things. One is inductance. This is caused by magnetic fields. The other is capacitance. This is caused by storing electric charge.

Impedance changes based on the frequency. Frequency is how fast the waves move. Engineers use a unit called the ohm to measure it. They can also use a tool called an impedance analyzer.

Scientists used math to study this. Oliver Heaviside named the term in 1886. Later, Charles Steinmetz showed how to use it for all AC circuits. This helped many engineers work with power. Today, we use impedance to study how electricity works in networks.

Electricity can move in different ways. Some electricity flows steadily in one direction. Other electricity moves in waves called alternating current, or AC.

In these AC circuits, parts can push back against the flow. This push back is called impedance. Impedance is more than just resistance. Resistance only measures how much a part slows down current. Impedance also includes something called reactance.

Reactance comes from two different things. One is inductance, which comes from magnetic fields. The other is capacitance, which comes from storing electric charge.

Impedance works in a very specific way. It is the total opposition to alternating current. It is made of both resistance and reactance combined. You can think of resistance as the real part. You can think of reactance as the imaginary part.

Engineers use math to show these two parts together. They often use a complex number to represent impedance. This helps them understand the magnitude and the phase. Magnitude tells you how strong the opposition is. Phase tells you how the voltage and current are timed.

Many smart people helped discover these ideas. Johann Victor Wietlisbach used complex numbers in 1879. He studied a tool called the Maxwell bridge. He did not call it impedance yet. Oliver Heaviside coined the term impedance in July 1886. He showed there was a way to use Ohm's law for AC.

Later, Arthur Kennelly wrote a paper in 1893. He used a triangle shape to show how parts add up. He followed ideas from John Ambrose Fleming from 1889. This made the math much easier to visualize.

Charles Proteus Steinmetz made these ideas even better. He worked on this in late 1893. He showed how to use impedance for all AC circuits. He used complex numbers for voltage and current too.

This helped engineers use math for many different problems. Impedance is measured in units called ohms. The symbol for impedance is Z. The opposite of impedance is called admittance. Admittance is measured in units called siemens. Engineers use tools called impedance analyzers to measure these values.

Understanding impedance helps us see how the world works. It connects to the simple Ohm's law you might know. In DC circuits, Ohm's law only uses resistance. In AC circuits, we just replace resistance with impedance.

This allows us to study big electrical networks. It also helps us understand how parts like resistors and capacitors work. A resistor has only real resistance. An inductor or a capacitor has purely imaginary reactance. This math keeps our lights on and our gadgets running.

In electrical engineering, impedance is the total opposition to alternating current (AC) in a circuit. While direct current (DC) circuits only deal with resistance, AC circuits are more complex. Impedance extends the concept of resistance to account for the behavior of waves. It is defined as the ratio of the complex sinusoidal voltage to the complex current flowing through a two-terminal circuit element. This concept is essential because it allows engineers to use linear laws to analyze electrical networks.

Impedance is composed of two distinct parts: resistance and reactance. Resistance is considered the real part of the impedance. It represents the opposition to current that results in energy loss. Reactance is the imaginary part of the impedance. Reactance is caused by two different physical effects. One is inductance, which involves the induction of voltages by magnetic fields. The other is capacitance, which involves the electrostatic storage of charge.

To manage these two parts, engineers represent impedance as a complex number. This can be done in two different ways. The polar form uses magnitude and phase. The magnitude represents the ratio of the voltage amplitude to the current amplitude. The phase, often written as a Greek letter, represents the timing difference between voltage and current. The Cartesian form uses a real part for resistance and an imaginary part for reactance. Engineers use the Cartesian form to add or subtract impedances. They use the polar form to multiply or divide them.

The history of impedance involves several key mathematical breakthroughs. In 1879, Johann Victor Wietlisbach used complex numbers to analyze the Maxwell bridge. He used exponential functions with imaginary exponents to avoid difficult differential equations. He found that voltage could be calculated by multiplying current by a complex number. However, he did not name this parameter "impedance." Oliver Heaviside coined the term "impedance" in July 1886. He later showed that an AC version of Ohm's law could exist.

Further developments made impedance math much more practical for engineers. In 1889, John Ambrose Fleming developed a graphical representation using a right-angle triangle. Arthur Kennelly published an influential paper in 1893 that expanded on this. Kennelly realized that this triangle was analogous to an Argand diagram for complex numbers. This allowed impedance to be added vectorially using algebra. Later in 1893, Charles Proteus Steinmetz generalized these ideas to all AC circuits. Steinmetz represented voltages and currents as complex numbers as well. This allowed engineers to use DC laws, like Ohm's and Kirchhoff's laws, in AC analysis.

Different components react to AC in very specific ways. An ideal resistor has purely resistive impedance, meaning it is purely real. In a resistor, the voltage and current are in phase, meaning they peak at the same time. Capacitors and inductors have purely imaginary reactive impedance. For a capacitor, the impedance decreases as the frequency increases. For an inductor, the impedance increases as the frequency increases. In these components, the voltage and current are 90 degrees out of phase. In a capacitor, the current leads the voltage. In an inductor, the current lags the voltage.

Impedance is measured in units called ohms, and its symbol is Z. The reciprocal of impedance is known as admittance. Admittance is measured in units called siemens. Engineers use specialized instruments called impedance analyzers to measure these values. Understanding impedance is vital for modern technology. It allows for the analysis of multiple port networks using an impedance matrix. It also connects simple DC principles to the complex reality of the alternating current that powers our world.