Ohm's Law — The Complete Physics Guide
Ohm's Law is the single most important relationship in electrical circuit analysis. Stated simply, it says that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. In equation form: V = IR. Despite its simplicity, this three-variable relationship underpins the design of every electronic device ever built.
Named after German physicist Georg Simon Ohm, who published the relationship in 1827, Ohm's Law was initially controversial — the scientific establishment was slow to accept it. Today it is as fundamental to electrical engineering as Newton's Laws are to mechanics.
Understanding V = IR
The three quantities in Ohm's Law each describe a distinct physical property of an electrical circuit. Voltage (V), measured in volts, is the electrical potential difference — the "pressure" that drives charge through the circuit. Current (I), measured in amperes, is the rate of charge flow — how many coulombs pass a point per second. Resistance (R), measured in ohms (Ω), is the opposition to current flow — determined by the material, dimensions, and temperature of the conductor.
A useful analogy is water flowing through a pipe: voltage is the water pressure, current is the flow rate, and resistance is the narrowness of the pipe. Increasing the pressure (voltage) increases the flow (current). Making the pipe narrower (higher resistance) reduces the flow for the same pressure. This hydraulic analogy, while imperfect, captures the essential physics.
Ohm's Law can be rearranged for any unknown: I = V/R to find current when voltage and resistance are known; R = V/I to find resistance when voltage and current are measured. This calculator handles all three rearrangements automatically.
Power Dissipation in Resistors
When current flows through a resistor, electrical energy is converted to heat. The rate of this energy dissipation — the power — is given by P = IV. Combining this with Ohm's Law gives two additional power formulas: P = I²R (power in terms of current and resistance) and P = V²/R (power in terms of voltage and resistance).
Understanding power is critical for safe circuit design. Every resistor has a power rating — the maximum rate at which it can safely dissipate heat. Exceeding this rating causes the resistor to overheat and fail. This is why component selection in electronics always involves checking not just resistance values but power ratings.
Worked Example 1 — Finding Current
Problem: A 12 V battery is connected to a 47 Ω resistor. What current flows, and how much power is dissipated?
Current: I = V/R = 12/47 = 0.255 A = 255 mA
Power: P = IV = 0.255 × 12 = 3.06 W (or P = V²/R = 144/47 = 3.06 W)
Worked Example 2 — Series and Parallel Circuits
Series circuit: Resistors in series add directly — total resistance R_total = R₁ + R₂ + R₃. Current is the same through each resistor; voltage divides proportionally.
Parallel circuit: Resistors in parallel combine as 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. Voltage is the same across each branch; current divides inversely proportional to resistance.
Problem: Two resistors of 100 Ω and 200 Ω are connected in parallel across a 6 V supply. Find total current and power.
1/R_total = 1/100 + 1/200 = 0.010 + 0.005 = 0.015 → R_total = 66.7 Ω
I_total = V/R_total = 6/66.7 = 90 mA
P = V²/R_total = 36/66.7 = 0.54 W
Ohmic vs Non-Ohmic Conductors
Ohm's Law holds for ohmic conductors — materials where resistance is constant regardless of current or voltage. Most metals at constant temperature are ohmic: copper, aluminium, gold, silver. For these materials, a graph of V against I is a straight line through the origin, with gradient equal to R.
Non-ohmic components do not obey Ohm's Law — their resistance changes with current, voltage, or temperature. Key examples: filament light bulbs (resistance increases with temperature), diodes (conduct in one direction only, with exponentially varying current), thermistors (resistance decreases as temperature increases), and LDRs (resistance decreases with light intensity).
Understanding which components are ohmic and which are not is crucial for circuit analysis. You can still define resistance as V/I for non-ohmic components (giving their "dynamic" or "differential" resistance at a specific operating point), but the simple V = IR relationship does not hold over a range of voltages.
Real-World Applications
LED current limiting: LEDs are non-ohmic and will draw too much current without a series resistor. The correct resistor value is R = (V_supply − V_LED)/I_LED — a direct application of Ohm's Law. Without this resistor, the LED instantly burns out.
Fuse ratings: Fuses are rated for the maximum current they allow before blowing. Using V = IR, you can calculate the maximum load resistance needed to stay within this rating for a given supply voltage — essential for safe electrical installation.
Power transmission: Electrical power is transmitted at very high voltages (400,000 V in the UK National Grid) to minimise current. Since power loss in transmission lines = I²R, reducing current by a factor of 10 reduces losses by a factor of 100. This is why transformers — which trade voltage for current — are fundamental to the electricity grid.
Resistivity and Factors Affecting Resistance
The resistance of a conductor depends on four factors: the material it is made of, its length, its cross-sectional area, and its temperature. The relationship is expressed through resistivity: R = ρL/A, where ρ (rho) is the resistivity of the material in ohm-metres (Ω·m), L is the length in metres, and A is the cross-sectional area in square metres.
This formula has intuitive physical explanations for each variable. Longer conductors have higher resistance because electrons must travel further and encounter more collisions. Wider conductors (larger A) have lower resistance because more charge can flow in parallel, just as a wider pipe carries more water. Different materials have different intrinsic resistivities: silver has the lowest resistivity of any metal (1.59 × 10⁻⁸ Ω·m), followed closely by copper (1.72 × 10⁻⁸ Ω·m). This is why copper is the standard choice for electrical wiring — it is the most cost-effective conductor after silver.
Temperature affects resistance in different ways for different materials. In metals, increasing temperature increases resistance — as ions vibrate more energetically, electrons encounter more collisions. In semiconductors like silicon, the opposite occurs — increasing temperature frees more charge carriers, decreasing resistance. This opposite behaviour is exploited in thermistors (temperature sensors) and makes semiconductor electronics temperature-sensitive.
Superconductivity is the extreme case: below a critical temperature (typically a few kelvin for conventional superconductors), resistance drops to exactly zero. Current can flow indefinitely without any voltage. Superconducting electromagnets — cooled by liquid helium — are used in MRI scanners, particle accelerators, and experimental maglev trains.
Kirchhoff's Laws — Extending Ohm's Law to Networks
Ohm's Law applies to individual components. To analyse complex circuits with multiple branches and loops, Kirchhoff's Laws extend the framework. Kirchhoff's Current Law (KCL) states that the algebraic sum of currents at any node (junction) is zero — charge is conserved, so what flows in must flow out. Kirchhoff's Voltage Law (KVL) states that the algebraic sum of voltages around any closed loop is zero — energy is conserved, so voltage gains equal voltage drops.
Together, Ohm's Law and Kirchhoff's Laws allow the complete analysis of any DC resistive circuit, no matter how complex. These three equations underpin the entire field of circuit analysis and are taught in every electrical engineering programme worldwide.