Ohm’s Law - Calculating Voltage, Current and Resistance

Voltage, current and resistance are the three fundamental electrical properties that govern every circuit. Ohm's Law defines the fixed relationship between them: voltage equals current multiplied by resistance (V = I × R). If you know any two of these values, you can calculate the third. For engineers selecting stepper motors, drivers, power supplies and wiring, understanding this relationship is the starting point for safe and effective circuit design.

This article explains what each property represents, how to apply Ohm's Law in practice and how to extend these calculations to power, with worked examples relevant to motor-driven systems.

Contents:

• What Voltage, Current and Resistance Mean
• Ohm's Law
• Worked Example: Calculating Motor Phase Current
• Worked Example: Selecting a Current-Limiting Resistor
• Extending to Power
• Common Pitfalls
• Wrap-up
• FAQs

What Voltage, Current and Resistance Mean

Before applying formulae, it helps to understand what each property actually describes.

• Voltage (V) is the electrical pressure that pushes charge through a circuit. It is measured in volts (V). A higher voltage means a greater force driving current from one point to another. In practical terms, voltage is determined by the power supply. A bench supply set to 12 V, a 24 V industrial rail or a 5 V USB connection each provide a different level of electrical pressure.
• Current (I) is the rate at which electrical charge flows through a conductor. It is measured in amperes, usually shortened to amps (A). Current is what actually does the work in a circuit by energising motor coils, illuminating LEDs or heating resistive elements. The amount of current flowing depends on both the voltage applied and the resistance in the circuit.
• Resistance (R) is the opposition a material or component offers to the flow of current. It is measured in ohms (Ω). Every conductor has some resistance. In a stepper motor, the resistance of each phase winding is a key specification because it directly affects how much current the motor draws at a given voltage.

Ohm's Law

Ohm's Law expresses the relationship between these three properties in a single equation that can be rearranged to solve for any unknown value:

• V = I × R - Voltage equals current multiplied by resistance
• I = V / R - Current equals voltage divided by resistance
• R = V / I - Resistance equals voltage divided by current

These three forms are the same equation rearranged. The Ohm's Law triangle is a common visual aid for remembering them: place V at the top, I at the bottom left and R at the bottom right. Cover the value you want to find and the remaining two show you the operation. Multiply if they are side by side, divide if one is above the other.

Worked Example: Calculating Motor Phase Current

A practical application of Ohm's Law is determining the current a stepper motor will draw from a given supply.

Consider a bipolar NEMA 17 stepper motor with a phase resistance of 3.3 Ω, connected to a 12 V supply with no current-limiting driver in the circuit. Applying Ohm's Law:

I = V / R = 12 / 3.3 = 3.64 A

This tells you the motor would attempt to draw 3.64 A per phase, well above the rated current for most NEMA 17 motors. In practice, a stepper motor driver limits current to the motor's rated value (for example, 1.2 A) by using pulse-width modulation (PWM) to chop the supply voltage. But understanding the relationship between supply voltage, winding resistance and resulting current is essential for selecting a driver with the right current rating and ensuring the power supply can deliver what the system needs.

Worked Example: Selecting a Current-Limiting Resistor

Ohm's Law is equally useful for simpler circuits. Suppose you want to power a 3.3 V indicator LED from a 12 V supply. The LED requires 20 mA (0.02 A) of forward current. The voltage that the resistor must drop is 12 - 3.3 = 8.7 V. Applying Ohm's Law:

R = V / I = 8.7 / 0.02 = 435 Ω

The nearest standard resistor value is 470 Ω, which would reduce the current slightly below 20 mA, a safe margin that protects the LED without noticeably affecting brightness.

Extending to Power

Once you can calculate voltage, current and resistance, you can also determine the power consumed or dissipated in a circuit. Power is measured in watts (W) and can be calculated using three related formulae:

• P = V × I - Power equals voltage multiplied by current
• P = I² × R - Power equals current squared multiplied by resistance
• P = V² / R - Power equals voltage squared divided by resistance

These are derived directly from Ohm's Law by substituting one variable for another.

Why power matters for motor systems

Power calculations help answer practical questions during system design. If a stepper motor draws 2 A per phase at 12 V, each phase consumes P = 12 × 2 = 24 W. A two-phase motor in full-step mode with both phases energised draws up to 48 W. This figure determines the minimum wattage rating for the power supply and influences thermal management decisions like heatsinking the driver, ventilating the enclosure or derating the motor for continuous duty.

Power dissipation in the motor windings also generates heat. The I²R losses in the coils are the primary source of heating in a stepper motor, which is why running a motor above its rated current shortens its lifespan even if it appears to function normally in the short term.

Common Pitfalls

• Confusing rated current with calculated current. A motor's datasheet specifies a rated current, which is the maximum continuous current the winding can handle without overheating. The current it actually draws depends on the supply voltage, winding resistance and driver settings. These are different numbers and must not be conflated.
• Ignoring back-EMF at speed. Ohm's Law gives you the static or DC current through a winding. When the motor is spinning, the rotor generates a back-EMF that opposes the supply voltage, effectively reducing the net voltage across the winding and thus reducing current. This is why stepper motors lose torque at higher speeds — less current flows through the coils as back-EMF rises.
• Overlooking wire resistance in long cable runs. In systems where the motor is mounted remotely from the driver, the resistance of the connecting cables adds to the total circuit resistance. Over long runs this can cause a meaningful voltage drop at the motor terminals, reducing available torque. Thicker gauge wire or a higher supply voltage compensates for this.

Wrap-up

Ohm's Law is the foundation of every electrical calculation in motor-driven systems. V = I × R lets you determine any one of voltage, current or resistance when the other two are known, and extending this to power (P = V × I) connects those calculations to real-world concerns like supply sizing, thermal management and component selection. For stepper motor applications, the most important takeaway is understanding how winding resistance, supply voltage and driver current limiting interact to determine the motor's actual operating current and power dissipation.

Further Reading

• How a Stepper Motor Works — anatomy, stepping methods and motor selection fundamentals
• Unipolar vs Bipolar Stepper Motors — winding configurations and their effect on torque and driver requirements
• Stepper Motor Drivers (0.3 A–2.0 A) — Accu's range of compatible driver boards.

FAQs:

Q: Does Ohm's Law apply to AC circuits?

A: Ohm's Law applies directly to purely resistive AC circuits. When a circuit includes inductors or capacitors, like a stepper motor winding does at higher frequencies, the concept of impedance replaces simple resistance. Impedance accounts for the additional opposition to current flow created by inductive and capacitive reactance. For the DC and low-frequency calculations involved in basic motor specification, Ohm's Law is sufficient.

Q: What happens if I connect a stepper motor directly to a power supply without a driver?

A: The motor will draw current determined by V / R with no regulation. For most stepper motors this produces a current far above the rated value, which will rapidly overheat the windings and can permanently damage the motor. Always use a current-limiting stepper motor driver.

Q: How do I find the resistance of a stepper motor winding?

A: The motor's datasheet will list resistance per phase in ohms. If no datasheet is available, you can measure it directly with a multimeter set to resistance mode (Ω) across the two leads of a single phase. Ensure the motor is disconnected from any driver or power supply before measuring.

Q: Why do stepper motor drivers use higher voltages than the motor's rated voltage?

A: A higher supply voltage allows the driver to push current into the inductive winding more quickly at the start of each step, improving high-speed torque. The driver's current chopping circuit then limits the average current to the motor's rated value, so the higher voltage does not cause overheating. This is why a motor rated at 3.3 Ω and 1.2 A is commonly paired with a 12 V or 24 V supply rather than the 3.96 V that Ohm's Law would suggest for 1.2 A steady-state.