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Ohm’s laws for direct and alternating current

To turn air into compressed air, you need power, and that power comes from electricity, either Alternating Current (AC) or Direct Current (DC). To understand how electricity flows through a compressor system, it helps to start with the basics. Ohm’s law explains the relationship between voltage, current, and resistance. In this article, we’ll break down these core concepts and how they apply to AC and DC systems powering compressed air.

What is ohm's law?

Ohm’s law explains how voltage, current, and resistance interact in an electrical circuit. It states that the current through a conductor increases with voltage and decreases with resistance, as long as temperature and other physical conditions stay the same.

 

Fact: Ohm’s law is named after German physicist and mathematician Georg Simon Ohm (1789-1854).

 

Voltage, current, and resistance

  • Voltage (V)
    Voltage is the electrical pressure that pushes current through a circuit. It’s measured in volts (V) and often described as the "force" that drives electricity from one point to another. Without voltage, there’s no movement of electrical charge, just like water won’t flow through a pipe without pressure.
  • Current (I)
    Current is the flow of electric charge and is measured in amperes (A). It represents how much electricity is actually moving through the circuit at any given moment. You can think of it like the volume of water flowing through a hose, the stronger the current, the more electricity is flowing.
  • Resistance (R)
    Resistance is the opposition to current flow within a material or circuit. It’s measured in ohms (Ω). The higher the resistance, the more it slows down the electrical current. Picture it like friction or a narrowing in a pipe that restricts how easily water, or in this case, electricity, can pass through.

What is ohm's law for direct current (DC)?

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship. In Direct Current systems, Ohm’s law is written as:

Ohm's law for direct current formula, V=I*R

Where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

A compressor motor draws 15 A of current and has a resistance of 8 Ω. Using Ohm’s law: V = I × R
V = 15 A × 8 Ω
V = 120 volts

If the power supply is below 120 V, the motor may not run correctly. This quick check helps spot electrical issues before they cause downtime.

DC circuit diagram

Direct current circuit diagram

Here’s a simple diagram showing the relationship between current (I), voltage (V), and resistance (R) in a circuit. With Ohm’s law, you can easily calculate any one of these values, as long as you know the other two.

The Ohm's triangle

Direct current circuit diagram

If you ever need a quick way to remember the different forms of Ohm’s law, the triangle below is a handy tool. It helps you easily solve for voltage (V), current (I), or resistance (R), depending on which values you have.

How to use the Ohm's triangle:
  1. Cover the unknown: Place your finger or hand over the variable you want to find (V, I, or R). 

  2. Perform the operation:
    • V (Voltage): If you cover V, I and R are left next to each other. This means V = I \* R. 
    • I (Current): If you cover I, V is above R. This means I = V / R.
    • R (Resistance): If you cover R, V is above I. This means R = V / I.

What is Ohm's law for alternating current (AC)?

An alternating current that passes through a coil gives rise to a magnetic flow. This flow changes magnitude and direction, just like an electric current.

When the flow changes, an emf (electromotive force) is generated in the coil, according to the laws of induction. This emf acts in the opposite direction of the connected pole voltage. This phenomenon is known as self-induction.

 

Self-induction in an AC circuit causes:

  • A phase displacement between the current and voltage

  • An inductive voltage drop

     

As a result, the unit’s resistance to AC (alternating current) appears greater than what would be measured in a DC (direct current) circuit.

 

Impedance in AC circuits

Impedance Z formula, Apparent resistance (Z) in relation to resistance (R) and inductive resistance (X)

Phase displacement is represented by the angle φ. Impedance, which combines resistance and reactance, is expressed with the formula:

Where:

  • Z = Impedance (Ω), or the total opposition to current

  • R = Resistance, the real component

  • X = Reactance, the inductive or capacitive component

Relation between Teactance (X) - Resistance (R) - Impedance (Z) - Phase displacement (φ)

Relation between Teactance (X) - Resistance (R) - Impedance (Z) - Phase displacement (φ)

Ohm’s law in AC circuits

Ohm's law for alternating current formula, V=I*Z

In AC systems, Ohm’s Law is written as:

Where:

  • V = Voltage (V)

  •  I = Current (A)

  • Z = Impedance (Ω)

Applications of Ohm's law

In everyday life: Using a phone charger

basic theory illustration mobile charger

Ohm’s law helps us understand how our everyday electronics function safely and efficiently. Take a phone charger, for example. When you plug it in, it delivers a set voltage, typically 5 volts (V), to your phone. The phone draws a certain amount of current based on its internal resistance and charging needs.

 

Let’s say your phone draws 1 ampere (A) of current.
Using Ohm’s law: R = V ÷ I

R = 5 V ÷ 1 A

R = 5 Ω

So, the charging circuit’s resistance is 5 ohms.

 

In essence, Ohm’s law gives engineers and technicians the ability to design, troubleshoot, and optimize even the smallest systems, like the one that powers your phone.

In industrial compressors: Checking motor coil current

an illustration about a basic theory article in the atlas copco air wiki

You’re inspecting a compressor motor that runs on 230 volts (V). Using a multimeter, you measure the coil resistance at 10 ohms (Ω).

 

Applying Ohm’s law: I = V ÷ R

I = 230 V ÷ 10 Ω 

I = 23 A

So, the motor should draw 23 amperes of current.

 

This is useful during maintenance or troubleshooting. If the measured current is significantly higher, it might indicate damage or overheating in the motor coil, helping prevent further failure or inefficiency.

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