Ohm''s Law

Calculate voltage, current and resistance using Ohm''s Law.

Inputs

U

I

R

Formula Interpretation

Ohm''s Law

U = I \times R

$U$ is voltage (V), $I$ is current (A), and $R$ is resistance (Ω). Ohm's Law states that the ratio of voltage to current is constant for a linear resistor at constant temperature — that ratio is the resistance. Established experimentally by Georg Simon Ohm in 1827, it is the foundation of DC circuit analysis.

Solve voltage

U = I \times R

Use when current $I$ (A) and resistance $R$ (Ω) are known. Commonly used to verify that the voltage drop across a conductor or load stays within the permitted range.

Solve current

I = \dfrac{U}{R}

Use when voltage $U$ (V) and resistance $R$ (Ω) are known. Useful for checking whether the operating current exceeds a component's rated value, especially with a known source impedance or current-limiting resistor.

Solve resistance

R = \dfrac{U}{I}

Use when voltage $U$ (V) and current $I$ (A) are known. Back-calculating resistance from measured values is a key fault-diagnosis technique: unexpected resistance indicates contact resistance, corrosion, or an out-of-tolerance component.

Electrical power

P = U \times I

$P$ is power (W), equal to $U$ × $I$ , or equivalently $I$ ² × $R$ , or $U$ ² / $R$ . The three forms suit different known-quantity combinations and are the primary input to resistor thermal derating and heat-sink calculations.

Knowledge Points

Linear I–V characteristic

For a linear resistor at constant temperature, current is proportional to voltage — the I–V graph is a straight line through the origin with slope equal to conductance $G = 1/R$ (siemens, S). When temperature rises, the lattice vibrations in a metal conductor increase, causing resistivity to increase and the I–V slope to fall slightly; for precision work the temperature coefficient $\alpha$ must be included.

Units and prefix conversion

Voltage uses V, current uses A, and resistance uses Ω — all quantities must share the same SI prefix level before substituting into the formula. Common engineering prefixes: current — mA ( $10^{-3}$ A), μA ( $10^{-6}$ A); resistance — kΩ ( $10^3$ Ω), MΩ ( $10^6$ Ω); voltage — mV, kV. For example, $I$ = 2.5 mA and $R$ = 4 kΩ must be converted to 0.0025 A and 4000 Ω, giving $U$ = 10 V.

Scope and non-linear devices

Ohm''s law applies only to ohmic (linear, purely resistive) elements. Diodes, LEDs, and transistors have non-linear I–V curves and require the Shockley diode equation or piecewise-linear models. MOSFETs operate differently in the linear (triode) and saturation regions. Thermistors (NTC/PTC) and varistors are inherently non-linear and should not be modelled as fixed resistors.

Relationship to Kirchhoff''s Laws

Ohm''s Law works alongside Kirchhoff''s Current Law (KCL: algebraic sum of currents at a node equals zero) and Kirchhoff''s Voltage Law (KVL: algebraic sum of voltages around a closed loop equals zero) to form the complete foundation of linear circuit analysis. Nodal analysis and mesh analysis both rely on applying Ohm''s Law to each branch resistance and then enforcing KCL or KVL to set up a system of simultaneous equations that yields all branch voltages and currents.

Worked Example

Given $I = 2.5\,\text{A}$ and $R = 4\,\Omega$ , solve the voltage $U = 10\,\text{V}$ and compute power $P = 25\,\text{W}$ .

Step 1 — Solve voltage

U = I \times R = 2.5 \times 4 = 10\,\text{V}

Step 2 — Solve power

P = U \times I = 10 \times 2.5 = 25\,\text{W}

Therefore, the circuit operates at $U = 10\,\text{V}$ and consumes $P = 25\,\text{W}$ .

Extended Knowledge

•Series and parallel applications in DC circuits：In DC circuits, Ohm's Law combines with series/parallel rules to solve any resistive network. For a voltage divider in series: $U_i = U \cdot R_i / R_{\text{total}}$ ; for a current divider in parallel: $I_i = I \cdot G_i / G_{\text{total}}$ . Voltage dividers set bias points in analog circuits; current-limiting resistors protect LEDs and logic-level converters.
•AC circuits and complex impedance：In AC circuits, Ohm's Law generalises to $\dot{U} = \dot{I} \cdot Z$ , where the complex impedance $Z = R + jX$ (Ω) has a resistive part $R$ and a reactive part $X = X_L - X_C$ . Inductive reactance $X_L = 2\pi f L$ and capacitive reactance $X_C = 1/(2\pi f C)$ . The impedance magnitude $|Z| = \sqrt{R^2 + X^2}$ and phase angle $\varphi = \arctan(X/R)$ determine whether voltage leads or lags current.
•Resistor power rating and derating：Standard resistor power ratings (1/8 W, 1/4 W, 1/2 W, 1 W, 2 W…) represent the maximum continuous dissipation. Good design practice derate to 50–70% of rated power to ensure long-term reliability and reduce thermal drift. Use whichever of $P = I^2 R$ , $P = U^2/R$ , or $P = UI$ is most convenient, then compare with the rated value and choose the next higher standard rating.
•Four-wire (Kelvin) resistance measurement：Standard two-wire resistance measurement includes the lead resistance in the result — a significant error for low-value resistors. The four-wire Kelvin method uses separate current-injection and voltage-sensing leads, placing the voltmeter directly across the device under test and eliminating lead-resistance errors entirely. This technique measures contact resistance and trace resistance down to the milliohm (mΩ) level and is standard in precision instrument calibration and battery-internal-resistance testing.
•Ohm''s Law in electrical fault diagnosis：Ohm''s Law is the primary tool for locating electrical faults: if the measured current under a known supply voltage is lower than expected, a hidden series resistance (loose connection, corroded contact, or partial break) exists in the path; if current is higher than expected, insulation breakdown or a partial short circuit is likely. Comparing measured versus calculated resistance values with a multimeter in de-energised circuits helps pinpoint faulty components quickly.

Ohm''s Law

Calculate voltage, current and resistance using Ohm''s Law.

Inputs

U

I

R

Formula Interpretation

Ohm''s Law

U = I \times R

Solve voltage

U = I \times R

Use when current $I$ (A) and resistance $R$ (Ω) are known. Commonly used to verify that the voltage drop across a conductor or load stays within the permitted range.

Solve current

I = \dfrac{U}{R}

Solve resistance

R = \dfrac{U}{I}

Electrical power

P = U \times I

Knowledge Points

Linear I–V characteristic

Units and prefix conversion

Scope and non-linear devices

Relationship to Kirchhoff''s Laws

Worked Example

Given $I = 2.5\,\text{A}$ and $R = 4\,\Omega$ , solve the voltage $U = 10\,\text{V}$ and compute power $P = 25\,\text{W}$ .

Step 1 — Solve voltage

U = I \times R = 2.5 \times 4 = 10\,\text{V}

Step 2 — Solve power

P = U \times I = 10 \times 2.5 = 25\,\text{W}

Therefore, the circuit operates at $U = 10\,\text{V}$ and consumes $P = 25\,\text{W}$ .

Extended Knowledge

•Series and parallel applications in DC circuits：In DC circuits, Ohm's Law combines with series/parallel rules to solve any resistive network. For a voltage divider in series: $U_i = U \cdot R_i / R_{\text{total}}$ ; for a current divider in parallel: $I_i = I \cdot G_i / G_{\text{total}}$ . Voltage dividers set bias points in analog circuits; current-limiting resistors protect LEDs and logic-level converters.
•AC circuits and complex impedance：In AC circuits, Ohm's Law generalises to $\dot{U} = \dot{I} \cdot Z$ , where the complex impedance $Z = R + jX$ (Ω) has a resistive part $R$ and a reactive part $X = X_L - X_C$ . Inductive reactance $X_L = 2\pi f L$ and capacitive reactance $X_C = 1/(2\pi f C)$ . The impedance magnitude $|Z| = \sqrt{R^2 + X^2}$ and phase angle $\varphi = \arctan(X/R)$ determine whether voltage leads or lags current.
•Resistor power rating and derating：Standard resistor power ratings (1/8 W, 1/4 W, 1/2 W, 1 W, 2 W…) represent the maximum continuous dissipation. Good design practice derate to 50–70% of rated power to ensure long-term reliability and reduce thermal drift. Use whichever of $P = I^2 R$ , $P = U^2/R$ , or $P = UI$ is most convenient, then compare with the rated value and choose the next higher standard rating.
•Four-wire (Kelvin) resistance measurement：Standard two-wire resistance measurement includes the lead resistance in the result — a significant error for low-value resistors. The four-wire Kelvin method uses separate current-injection and voltage-sensing leads, placing the voltmeter directly across the device under test and eliminating lead-resistance errors entirely. This technique measures contact resistance and trace resistance down to the milliohm (mΩ) level and is standard in precision instrument calibration and battery-internal-resistance testing.
•Ohm''s Law in electrical fault diagnosis：Ohm''s Law is the primary tool for locating electrical faults: if the measured current under a known supply voltage is lower than expected, a hidden series resistance (loose connection, corroded contact, or partial break) exists in the path; if current is higher than expected, insulation breakdown or a partial short circuit is likely. Comparing measured versus calculated resistance values with a multimeter in de-energised circuits helps pinpoint faulty components quickly.