Ohm's Law is the most important equation in all of electrical engineering. It is simple, used all the time, and underpins the physics of circuits to ensure we are sizing our conductors and equipment correctly. Ohm's Law can be stated as follows:
V = I Z
Where:
V is the voltage across an impedance in Volts
I is the current flowing through an impedance in Amperes
Z is the value of the complex impedance in Ohms
Simple Circuit Showing Ohm's Law
Let's break down each of the variables in Ohm's Law with some more detail.
Voltage - Voltage describes the electrical potential of a source and is only well-defined between two points. In Ohm's Law, the voltage V is applied across the load impedance Z. Here are some common misconceptions we need to eliminate right now about voltage:
Voltage is not defined for a point by itself. It's common in power systems that we say "the voltage of the line" or the "system voltage", but that is always with an understanding that we are measuring between a certain point (say an energized line) and the neutral/ground point referenced to zero Volts. So remember, voltage is always across something.
The voltage in Ohm's Law refers to the root-mean-square (rms) voltage of an AC waveform. In other words, think nominal system voltage levels like the 120VAC in your house. In reality, the AC voltage waveform is varying all the time and the peak value will actually exceed the nominal number at times.
Current - Current describes the movement of electrons through some point in space. In Ohm's law, the current I flows because a voltage V is present across the impedance. Just like AC voltages, AC currents are varying all the time and will actually have peak values that exceed nominal rms values. Current determines the heat produced in a circuit, and is the basis for ampacity limitations described in many of the other articles on Breaker & Fuse.
Impedance - Impedance is just what its name says: it is an impediment to the flow of current when a voltage is applied. As you can see from Ohm's Law, when the voltage goes up the current flowing through an impedance will also go up. Impedance is a complex number consisting of a real part, resistance, and an imaginary part, reactance.
Z = R + j X
Where:
Z is the complex impedance in Ohms
R is the resistance in Ohms
X is the reactance in Ohms
j is the imaginary number √(-1)
Resistance is due to the fact that materials aren't perfect conductors or insulators. If a voltage, AC or DC, is applied across a material, that material's chemical properties and temperature will lead to a resistance that limits the flow of current. In an ideal conductor, electrons would all move nicely, but in a real conductor there are obstacles in the path that prevent flow. Unfortunately, due to a phenomenon known as the skin effect, the AC resistance of a conductor is higher than the DC resistance. Higher frequencies make the skin effect worse.
Reactance is only defined for AC systems. Reactance is an effect created by time-varying fields. Magnetic fields (from electric currents) create inductances, and electric fields (from electric charge) create capacitances. Reactances are dependent upon the configuration of the system. If conductors are spaced differently, systems will have different reactances. Moreover, the materials in the vicinity of a system impact the reactance. You can see this by looking at the reactances for common cable configurations in NEC Chapter 9 Table 9 as an example.
Often, electrical engineers are only concerned with magnitudes in a power system and not the particular phase. Under these conditions, we can convert the impedance to its magnitude:
| Z | = √( R^2 + X^2 )
Computing resistances and reactances from scratch is difficult to do. For equipment like transformers, this information should be taken from the manufacturer based on their final testing. There are often significant tolerances in values that can lead to deviations from specified numbers. Motors have time-varying impedance, and their behavior is usually identified at certain load conditions such as starting (also known as locked-rotor) and full-load. For conductors, values are easier to compute, but it is still a best practice to take information from the supplier/manufacturer. If this information is not available, then using NEC Chapter 9 Table 9 as a starting point can be very helpful. Actual determination of resistances and reactances requires careful application of Maxwell's equations and simplifications can often lead to considerable error.
Analogy - Ohm's Law is often analogized to a hose. You can think of the pressure in the hose as the voltage in the electrical circuit, current as the flow of water, and impedance as the nozzle. There can be pressure in the hose with no flow, and altering the opening of the nozzle will change how much water flows out. An electrical circuit is no different: you can have voltage with no current (an open circuit), and altering the impedance of the load will alter how much current flows to it.
Example: What is the magnitude of the current that will flow through a load with a resistance of 1 Ohm and a reactance of 2 Ohms when the applied voltage is 120V?
Solution: Start by drawing a picture. The same image from above is copied below with values provided.
In order to determine the current flowing through the load, we need to rewrite Ohm's Law into a more useful form:
V= I Z becomes I = V / Z
Next, since we're only worried about magnitudes, we can neglect the phases of the complex impedance, voltage, and current:
| I | = | V | / √( R^2 + X^2 )
Lastly, we just need to plug in our values to get an answer:
120 / √( 1^2 + 2^2 ) = 120 / √( 5 ) = 53.7 A
So, for our load of 1+2j Ohms, we can expect a magnitude of 53.7A of current to flow.
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