Ohm's Law Calculator

What's the key thing to understand about The Triangle?

Ohm's Law describes the fundamental relationship between voltage (V, in volts), current (I, in amps), and resistance (R, in ohms) in an electrical circuit. The core equation is V = I × R: voltage equals current multiplied by resistance. Rearranging gives the other two forms: I = V ÷ R (current equals voltage divided by resistance) and R = V ÷ I (resistance equals voltage divided by current). The 'Ohm's Law triangle' is a memory aid — write V at the top with I and R below; cover the quantity you want, and the position of the other two tells you whether to multiply or divide. Power (P, in watts) extends the law: P = V × I, and by substitution P = I² × R = V² ÷ R. These give you four interlinked quantities (voltage, current, resistance, power), and knowing any two lets you find the others. A worked example: a 12V supply across a 4-ohm resistor drives a current of I = 12 ÷ 4 = 3 amps, dissipating P = 12 × 3 = 36 watts. These relationships describe the behaviour of every simple resistive circuit and underpin practically all electrical and electronic design, from sizing a current-limiting resistor for an LED to understanding why thick cables are needed for high-current loads.

What do I need to know about Everyday Application?

Ohm's Law isn't just theory — it governs everyday electrical situations and helps explain device ratings and safety limits. A UK household circuit at 230V protected by a 13A fuse (as in a standard plug) can safely supply up to P = 230 × 13 ≈ 2,990 watts, which is why a 3kW kettle is about the most powerful single appliance on a standard plug. A USB charger outputting 5V at 2A delivers P = 5 × 2 = 10 watts. When choosing a resistor to protect an LED, you use Ohm's Law: if your supply is 5V, the LED drops about 2V and needs around 20mA (0.02A), the resistor must drop the remaining 3V, so R = 3 ÷ 0.02 = 150 ohms. Cable sizing depends on it too — current causes heating proportional to I²R, so high-current circuits need thicker (lower-resistance) cable to avoid overheating, and this is why long cable runs suffer voltage drop. Battery life, speaker impedance matching, fuse selection, and power-supply design all rest on these relationships. Understanding Ohm's Law lets you predict how much current a device will draw, whether a circuit is within safe limits, and how components will behave together.

What should I know about Limitations?

Ohm's Law, in its simple form, applies to 'ohmic' (linear) components — chiefly resistors — where resistance stays constant regardless of the voltage or current. For these, a graph of voltage against current is a straight line through the origin, and the relationships V = IR hold exactly. But many real components are 'non-ohmic', and the simple law doesn't fully describe them. A filament light bulb's resistance rises sharply as it heats up, so its current doesn't increase proportionally with voltage. Diodes conduct in only one direction and have a non-linear voltage-current curve with a 'turn-on' threshold. Transistors, thermistors (resistance varies with temperature), and LDRs (resistance varies with light) all change resistance with conditions. Semiconductors generally are non-linear. Ohm's Law also assumes direct current (DC) or treats AC simply; in AC circuits with capacitors and inductors, you need the broader concept of impedance (which includes frequency-dependent reactance) rather than plain resistance. And at extremes — very high voltages, very low temperatures (superconductivity), or very high frequencies — additional physics applies. For everyday resistive circuits, Ohm's Law is accurate and indispensable; for non-ohmic components and AC analysis, it's a starting point that needs extending. Knowing where it applies — and where it doesn't — is part of using it correctly.

What's the key thing to understand about Units and Significant Figures?

Science calculations require consistent units throughout. Mixed units (some in metres, some in centimetres) are the most common source of errors. Always check: are all values in SI units (metres, kilograms, seconds, kelvin) before substituting into formulas? The number of significant figures in an answer should not exceed the least precise measurement used in the calculation. When quoting a result, scientific notation (e.g. 3.7 x 10 to the power 4) avoids ambiguity about significant figures and makes very large or very small values easier to read and compare.

What's the difference between Ohmic and Non-Ohmic Conductors?

An ohmic conductor — a metal wire at constant temperature is the textbook example — has resistance that stays constant regardless of current, producing a straight-line voltage-current graph through the origin that exactly obeys V = IR at every point. A non-ohmic component, such as a diode, filament lamp, or thermistor, has resistance that itself changes with current or temperature, producing a curved V-I graph instead: a filament lamp's resistance rises sharply as it heats up and glows, which is why its V-I curve flattens out at higher currents rather than continuing in a straight line.

Worked Example: Finding Current, Voltage, and Resistance

A 12 V battery is connected to a resistor with resistance R = 4 Ω. Using Ohm's law, V = IR, the current flowing through the circuit is I = V/R = 12/4 = 3 A. The power dissipated by the resistor can be found two equivalent ways: P = VI = 12 × 3 = 36 W, or P = I²R = 3² × 4 = 9 × 4 = 36 W — both give the same answer, which is a good way to double-check a calculation. If the same battery were instead connected to a resistor of 12 Ω, the current would drop to I = 12/12 = 1 A, and the power would fall to P = 12 × 1 = 12 W — a reminder that for a fixed voltage source, tripling the resistance cuts both the current and the power, though not by the same factor (power drops with the square of current, so it falls faster than the current itself does when resistance increases).

Table: Ohm's Law Applied to Common Household Devices

Every plug-in device has an effective resistance that can be worked out from its rated voltage and power, using R = V/I where I = P/V. The table below shows typical household devices with realistic values.

Notice that the toaster and kettle, which draw the most power, have the lowest resistance — for a fixed voltage, lower resistance always means higher current and higher power draw, which is also why high-power appliances need thicker wiring to avoid overheating.

Series and Parallel Resistance Combinations

Ohm's law applies to a whole circuit as well as to a single resistor, but first the combined resistance of multiple resistors has to be found, and that calculation depends on whether they're in series or parallel. For resistors in series, total resistance simply adds: R_total = R₁ + R₂ + R₃ + .... Three resistors of 2 Ω, 3 Ω, and 5 Ω in series give R_total = 2 + 3 + 5 = 10 Ω. For resistors in parallel, the reciprocals add instead: 1/R_total = 1/R₁ + 1/R₂ + .... Two resistors of 6 Ω and 3 Ω in parallel give 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so R_total = 2 Ω — notably less than either individual resistor, because parallel paths always give current more ways to flow, lowering the overall resistance. Once the combined resistance is known, Ohm's law applies to the whole network exactly as it would to a single resistor: a 12 V source across that 2 Ω parallel combination would draw a total current of I = 12/2 = 6 A, which then splits between the two branches according to each branch's own resistance.