Ohm's Law states that the voltage across a resistive element equals the current through it multiplied by its resistance: V = I × R. It is one of the foundational relationships in circuit analysis and applies directly to purely resistive elements at a given operating point.
In practice
Ohm's Law appears constantly in embedded hardware design. Calculating a current-limiting resistor for an LED, sizing a pull-up resistor on an I2C bus, or determining the voltage drop across a sense resistor all reduce to a direct application of V = I × R. Getting these values wrong -- for example, omitting the resistor or using the wrong supply voltage in the calculation -- is one of the most common causes of burned GPIO pins and failed peripherals on a first board bring-up.
The law is equally useful when rearranged. I = V / R lets you calculate how much current a load will draw from a supply rail, which feeds directly into power budget calculations and the selection of voltage regulators, bypass capacitors, and protection fuses. R = V / I is used when measuring a known current with a known voltage drop to extract resistance, a technique used in low-side current sensing with a shunt resistor.
Ohm's Law applies cleanly to resistors, but embedded engineers must remember it describes a linear, memoryless relationship. Semiconductor devices -- diodes, MOSFETs, BJTs -- are not ohmic over their full operating range. A MOSFET in its triode (linear) region can be approximated as a resistor with value R_DS(on), and Ohm's Law then estimates conduction loss (P = I² × R), but that R_DS(on) itself varies with gate voltage and temperature. The blog post "How to Read a Power MOSFET Datasheet" covers how to extract and derate these parameters correctly.
Parasitic resistances -- trace resistance, contact resistance, connector resistance -- are easily overlooked but become significant at high currents or when making precision measurements. A milliohm of resistance is invisible at 1 mA but drops 100 mV at 100 A. Kelvin (four-wire) sensing is the standard technique for removing lead and contact resistance from precision resistance measurements, as discussed in the post "Someday We'll Find It, The Kelvin Connection."
Frequently asked
Does Ohm's Law apply to capacitors and inductors?
Not in the DC resistive sense.
Capacitors and
inductors are reactive elements described by V = L × dI/dt and I = C × dV/dt, respectively. In AC or transient analysis, their behavior is captured using impedance (Z) in the generalized form V = I × Z, which reduces to Ohm's Law for the purely resistive case where Z = R.
How do I use Ohm's Law to size a pull-up resistor?
Determine the supply voltage, the minimum acceptable logic high voltage, and the maximum leakage or sink current the pulled-up line must drive. Use R = V / I to find the maximum resistor value that still delivers adequate current. Then check that the resulting current at the low state does not exceed what the driving device can sink while staying within its VOL spec. Lower resistance means more current and a stronger
pull-up but higher idle power draw.
Can I use Ohm's Law to calculate power dissipation?
Yes. Combining Ohm's Law with P = V × I gives two useful forms: P = I² × R and P = V² / R. These are standard for calculating resistor dissipation,
MOSFET conduction loss, and trace heating. Make sure to use RMS values for current and voltage when dealing with non-DC waveforms.
What is a zero-ohm resistor, and how does Ohm's Law apply to it?
A zero-ohm resistor is a wire-wound or metal-strip component in a standard resistor package, used as a jumper on PCBs. Theoretically V = I × 0 = 0 V across it, but real zero-ohm resistors have a small but nonzero resistance (often specified as a maximum, e.g., 50 mΩ), which matters at high currents. The blog post "Short Takes (EE Shanty): What shall we do with a zero-ohm resistor?" covers their practical uses in layout and configuration.
Why does Ohm's Law seem to break down when I measure a diode or transistor?
Diodes and transistors are nonlinear devices whose I-V relationship is governed by the Shockley equation and
transistor models, not a fixed resistance. Ohm's Law still applies locally -- at any given operating point you can define a small-signal or incremental resistance -- but that resistance changes with operating conditions, so you cannot use a single R value across the full operating range as you would with a resistor.
Differentiators vs similar concepts
Ohm's Law (V = IR) describes the behavior of resistive elements and is a special case of the more general relationship V = IZ, where Z is complex impedance. Impedance extends the concept to
capacitors,
inductors, and combinations thereof in AC circuits. Ohm's Law is also distinct from Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL), which govern how voltages and currents relate across entire networks rather than across individual elements.
