How to Use Ohm's Law (V = IR): Formula, Units & Worked Examples

Use Ohm's law V = IR with clear mA and kΩ conversions and homework examples. Check every answer with a free Ohm's law calculator for voltage, current, and resistance.

What Ohm's Law Means

Ohm's law links three circuit quantities: voltage (V), current (I), and resistance (R). For an ohmic resistor, they stay in proportion: V = I × R. Raise the voltage across a fixed resistor and the current rises. Raise the resistance at fixed voltage and the current falls.

Introductory physics and electronics problems use this relationship constantly. Once you know any two values, the third is fixed. That is why a calculator that rearranges V = IR, I = V/R, and R = V/I is enough for most homework checks.

If you already have two values and only need a checked number, open the free Ohm's law calculator first, then return here for unit traps and worked examples that usually cost marks.

The Formula V = IR and Rearrangements

Start from V = I × R. Three forms cover almost every school problem:

V = I × R — find voltage when current and resistance are known.

I = V / R — find current when voltage and resistance are known.

R = V / I — find resistance when voltage and current are known.

Isolate the unknown, convert units to volts, amperes, and ohms, then multiply or divide. The SI answer units are V, A, and Ω.

When Ohm's Law Applies

Use Ohm's law when the problem treats the component as an ohmic resistor: a single R that does not change with the voltage in the range you care about. Metal-film resistors in lab kits are the usual case.

Do not force a single R onto every device. Diodes, LEDs, and many semiconductors are non-linear. If the question gives a diode curve or says “non-ohmic,” Ohm's law alone is not the whole model.

Unit Traps That Break Answers

Milliamps vs amperes

Convert mA to A before dividing (÷ 1000). A 30 mA current is 0.030 A. Using 30 in R = V/I with volts produces an answer 1000× too small.

Kilo-ohms vs ohms

Convert kΩ to Ω (× 1000) unless every quantity is consistently in kilo-units and you track that carefully. 2.2 kΩ is 2200 Ω.

Confusing power with Ohm's law

Power uses P = V I (and P = I²R, P = V²/R). If the unknown is watts, solve Ohm's law for the missing V, I, or R only when needed, then move to power—or use the electric power calculator directly.

Worked Example 1: 12 V Across 4 Ω

A 4.0 Ω resistor is connected across a 12 V DC supply. Find the current.

I = V / R = 12 / 4.0 = 3.0 A.

Sanity check: at the same 12 V, a 2 Ω resistor would draw 6 A—twice the current for half the resistance.

Worked Example 2: 9 V and 30 mA

A component draws 30 mA from a 9.0 V battery. Find its resistance, assuming an ohmic model.

Convert: 30 mA = 0.030 A. R = V / I = 9.0 / 0.030 = 300 Ω.

If you forget the conversion and compute 9 / 30 = 0.3 Ω, the answer is wrong by three orders of magnitude—a classic mark loss.

Ohm's Law vs Voltage Dividers and Networks

Ohm's law handles one resistance relationship at a time. When two resistors share a supply and you need the voltage across one of them, use a voltage divider. When several resistors combine first, find the equivalent resistance, then apply Ohm's law to the total.

For split supplies across two resistors, use the voltage divider calculator. For series or parallel pairs, use the series-parallel resistance tool, then return to Ohm's law for current or voltage.

Common Mistakes

Leaving current in mA while resistance is in ohms.

Treating kΩ as Ω inside V = IR.

Writing I = R / V instead of I = V / R.

Applying one fixed R to a clearly non-ohmic device.

Mixing power formulas with Ohm's law without stating which unknown you want.

Sanity check: household USB-scale currents are often tens to hundreds of mA; amp-scale currents through small resistors imply large power and heat.

Check Your Work with Free Calculators

Once the method is clear, verify the arithmetic. The Ohm's law calculator solves for V, I, or R with visible steps so you can confirm the substitution.

Ohm's law calculator — voltage, current, or resistance from V = IR.

Electric power calculator — when the unknown is watts (P = VI, I²R, V²/R).

Voltage divider calculator — two-resistor output voltage.

Series & parallel resistance calculator — equivalent R before Ohm's law.

Master V = IR with clean ampere and ohm units. That habit carries into almost every introductory circuit problem.

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