Every electronic device you use — from the phone in your pocket to the lamp on your desk — operates according to a single elegant relationship: Ohm's Law. This law states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance. It is the foundational equation of circuit analysis and electrical engineering, and understanding it unlocks the physics behind virtually every electrical device ever built.
Ohm's Law: The current I through a conductor is proportional to the voltage V across it and inversely proportional to the resistance R:
V = IR
V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). Equivalently: I = V/R and R = V/I.
The Three Quantities: Voltage, Current, and Resistance
Voltage (V): the electric potential difference between two points, measured in volts (V). It is the "pressure" that drives charge through a circuit. A 9 V battery maintains a 9-volt potential difference between its terminals. A UK mains supply provides 230 V AC. Voltage is the cause; current is the effect.
Current (I): the rate of flow of electric charge through a conductor, measured in amperes (A). 1 A = 1 coulomb of charge passing a point per second. In a copper wire, it is the collective drift of free electrons (though by convention current is defined as flowing from + to −, opposite to electron flow). A smartphone charger typically draws ~1–2 A; a kettle element draws ~10 A.
Resistance (R): the opposition to current flow, measured in ohms (Ω). It arises from collisions between charge carriers and the atomic lattice of the conductor. At a given voltage, higher resistance means less current. Resistance depends on material (resistivity ρ), length L, and cross-sectional area A: R = ρL/A. A longer, thinner wire has higher resistance than a short, thick one of the same material.
Ohm's Law Formula
The three forms of Ohm's Law:
Remember them using the triangle: cover V to get IR; cover I to get V/R; cover R to get V/I.
Worked Examples
Example 1: Finding current
A 12 V battery is connected across a 60 Ω resistor. What current flows?
Example 2: Finding voltage
A current of 3 A flows through a 15 Ω resistor. What is the voltage across it?
Example 3: Finding resistance
A 240 V supply drives 4 A through a heating element. What is its resistance?
Resistors in Series and Parallel
Series: components connected end-to-end so the same current flows through each. The same current I flows through each resistor; voltages add.
Example: 10 Ω, 20 Ω, and 30 Ω in series: R_total = 60 Ω. If 12 V is applied, I = 12/60 = 0.2 A through all three.
Parallel: components connected side-by-side so the same voltage appears across each. The same voltage V appears across each resistor; currents add.
Example: 10 Ω and 20 Ω in parallel: 1/R = 1/10 + 1/20 = 3/20, so R_total = 6.67 Ω — always less than the smallest individual resistance.
| Property | Series circuit | Parallel circuit |
|---|---|---|
| Current | Same through all components | Splits between branches |
| Voltage | Splits across components | Same across all components |
| Total resistance | Increases: R = R₁ + R₂ + ... | Decreases: 1/R = 1/R₁ + 1/R₂ + ... |
| If one component fails | Circuit breaks — all stop | Other branches continue |
Electrical Power
Power dissipated in a resistor — the rate of energy transfer to heat — is:
where P is in watts (W). A 60 Ω kettle element running at 230 V dissipates P = 230²/60 = 882 W ≈ 0.88 kW. Over 1 hour: energy = 0.88 kWh, costing roughly 30p at UK electricity prices. The relationship P = I²R explains why power lines transmit electricity at high voltages (tens of thousands of volts): for the same power, higher voltage means lower current, and P_loss = I²R_line is reduced dramatically.
When Ohm's Law Does Not Apply
Ohm's Law holds for ohmic conductors — materials where resistance remains constant as voltage or current changes. Most metals at constant temperature are ohmic.
Non-ohmic devices include:
Diodes: allow current in one direction only. The current-voltage curve is highly non-linear — almost zero below the forward voltage threshold (~0.7 V for silicon), then rising steeply.
Thermistors: resistance changes significantly with temperature. NTC (negative temperature coefficient) thermistors decrease in resistance as temperature rises — used in temperature sensing and self-resetting fuses.
Light-dependent resistors (LDRs): resistance decreases in bright light. Used in automatic street lamps and camera exposure meters.
Filament bulbs: resistance increases as the filament heats up (metals have positive temperature coefficient). A "cold" bulb has much lower resistance than when at operating temperature.
Frequently Asked Questions
What is Ohm's Law?
Ohm's Law states that the current through a conductor is proportional to the voltage across it and inversely proportional to its resistance: V = IR. V is voltage (volts), I is current (amperes), and R is resistance (ohms). It holds for ohmic conductors at constant temperature.
What is the formula for Ohm's Law?
V = IR, where V is voltage (V), I is current (A), and R is resistance (Ω). Rearranged: I = V/R (to find current) and R = V/I (to find resistance). All three forms are equivalent — choose which to use based on which quantity you want to find.
What is the unit of resistance?
Resistance is measured in ohms (Ω), named after Georg Simon Ohm who formulated the law in 1827. 1 ohm = 1 volt per ampere (1 Ω = 1 V/A). Resistors commonly range from 1 Ω (low resistance, like a heating element) to millions of ohms (megaohms, MΩ) in sensitive electronics.
What is the difference between series and parallel circuits?
In a series circuit, components are connected end-to-end: same current through all, voltages add, total resistance is the sum of individual resistances. In a parallel circuit, components are connected side-by-side: same voltage across all, currents add, total resistance is less than the smallest individual resistance.
Does Ohm's Law always apply?
No. Ohm's Law applies to ohmic conductors — materials where resistance is constant. Non-ohmic devices include diodes (highly non-linear current-voltage curves), thermistors (resistance changes with temperature), LDRs (resistance changes with light), and filament bulbs (resistance changes as filament heats up). For non-ohmic devices, R = V/I still gives the resistance at that operating point, but it is not constant.
Why is electrical power transmitted at high voltage?
Power loss in transmission lines is P_loss = I²R. For a given power P = IV, higher voltage V means lower current I. Lower current means dramatically less power lost as heat in the resistance of the cables. A 10× increase in voltage gives 100× reduction in transmission losses. This is why national grids use 275,000 V–400,000 V and step down to 230 V for homes via transformers. The physics of these circuits connects directly to electric charge and Coulomb's law and to electric field and potential.
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Written by
Dr. Sarah KimThermodynamics researcher with a PhD from MIT, specializing in statistical mechanics and energy transfer. Passionate about connecting molecular physics to everyday phenomena.
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