The relationship between voltage, current, and resistance
Ohm’s law connects three electrical quantities in a simple linear relationship:
V = I × R
V is potential difference in volts, I is electric current in amperes, and R is resistance in ohms. Knowing any two lets you calculate the third by rearranging the equation.
The equation describes an ohmic element under stable physical conditions. It is not a claim that every electrical device has one constant resistance in all situations.
Solving for voltage
Voltage is current multiplied by resistance:
V = I × R
If 2 amperes flow through 12 ohms, the voltage is 24 volts. The voltage represents energy transferred per unit charge between two points.
Sign matters in circuit analysis. A negative calculated voltage means the actual polarity is opposite the reference polarity chosen before solving. It does not mean the physical quantity is invalid.
Solving for current
Divide voltage by resistance:
I = V ÷ R
Applying 12 volts across 6 ohms produces 2 amperes in the ideal relationship. Resistance must not be zero in this rearrangement because division by zero is undefined.
A real source and wiring have internal resistance and current limits. Connecting a nominal zero-resistance path can produce a dangerous short circuit rather than an infinite current because the rest of the circuit constrains the result while dissipating intense heat.
Solving for resistance
Divide voltage by current:
R = V ÷ I
If a measured device has 10 volts across it while 0.5 amperes flow, the ratio is 20 ohms at that operating point.
For a nonlinear device, this ratio is static or chord resistance at the measured point. The small-signal or dynamic resistance relates a small voltage change to a small current change and can have another value.
SI electrical units
The volt, ampere, ohm, and watt are related SI units. The ampere is an SI base unit. A volt is a joule per coulomb and can also be expressed as a watt per ampere. An ohm is a volt per ampere.
1 Ω = 1 V/A
1 W = 1 V·A
Prefixes scale units by powers of ten. One milliampere is 0.001 A, one kilohm is 1,000 Ω, and one megohm is 1,000,000 Ω. Convert prefixed values to a consistent base before applying the formula.
For example, 5 V across 10 kΩ gives 5 ÷ 10,000 = 0.0005 A, which is 0.5 mA.
Electrical power
Power is the rate of electrical energy transfer:
P = V × I
Combining this equation with Ohm’s law produces two equivalent resistor formulas:
P = I²R
P = V²/R
A 12-ohm resistor carrying 2 A dissipates 48 W. The same result comes from 24 V × 2 A or 24² ÷ 12.
The calculator reports this ideal power alongside the solved variable. A component should not be selected to operate continuously at the exact edge of its power rating without considering manufacturer derating, temperature, airflow, pulse duration, and required reliability.
Ohmic and non-ohmic behaviour
An ohmic element has a linear voltage-current relationship under fixed conditions. Doubling applied voltage doubles current, so the ratio V/I stays constant.
Many real devices are not ohmic across their full range. A diode conducts very differently by polarity and voltage. A filament lamp’s resistance rises as it heats. A thermistor is designed to change resistance with temperature. Semiconductor junctions, batteries, motors, and gas-discharge devices have state-dependent behaviour.
Ohm’s law remains useful locally or inside a more complete model, but one resistance number may not predict another operating point.
Temperature effects
Conductor resistance usually changes with temperature. For a limited range, a linear approximation is often written:
R = R₀[1 + α(T − T₀)]
The temperature coefficient α depends on material and reference conditions. Copper resistance generally rises with temperature; some semiconductor materials behave differently.
Self-heating couples power back into resistance. Current creates heat, temperature changes resistance, and the new resistance changes current. A calculation using a room-temperature value can therefore differ from the settled operating condition.
Use manufacturer curves or a thermal model when the effect matters.
Series resistors
Ideal resistors in series carry the same current. Their voltage drops add, so equivalent resistance is the sum:
Rseries = R₁ + R₂ + …
Two resistors of 4 Ω and 8 Ω in series equal 12 Ω. With 24 V across the pair, current is 2 A. The drops are 8 V and 16 V respectively.
The division of voltage in a series network leads directly to the voltage-divider formula. A connected load changes that division because it changes the effective lower resistance.
Parallel resistors
Ideal parallel branches share the same voltage and their currents add:
1/Rparallel = 1/R₁ + 1/R₂ + …
For two resistors:
Rparallel = R₁R₂ ÷ (R₁ + R₂)
Equivalent parallel resistance is smaller than the smallest branch resistance because the network provides more paths for current.
Do not add parallel resistance values directly. That rule belongs to series connections.
Worked examples
A sensor circuit has 3.3 V across 1 kΩ. Current is 3.3 ÷ 1,000 = 0.0033 A, or 3.3 mA. Power is 3.3 × 0.0033 = 0.01089 W, about 10.89 mW.
A heater draws 5 A from a 120 V source. Its operating resistance under the simple model is 24 Ω and electrical power is 600 W. Cold resistance can differ from hot operating resistance.
A resistor must carry 20 mA from a 9 V drop. Converting 20 mA to 0.020 A gives R = 9 ÷ 0.020 = 450 Ω. The ideal power is 0.18 W, so component choice should consider an appropriate rating above that value.
Measurement and instrument loading
A voltmeter is connected in parallel and ideally has infinite input resistance so it draws no current. Real meters have finite input impedance and can alter high-resistance circuits.
An ammeter is connected in series and ideally has zero resistance. Real meters introduce a burden voltage and have current limits and fuses.
Resistance should normally be measured with power removed and capacitors safely discharged. Measuring resistance in a connected network can read parallel paths rather than the isolated component.
Follow instrument category ratings and safe measurement practices, especially around mains, batteries with high fault current, and stored energy.
Source resistance and voltage drop
An ideal voltage source maintains its voltage at any current. A real source has internal impedance and output limits. Wiring and connectors add resistance.
Under load, current through those resistances creates voltage drop and heat. A battery’s terminal voltage can fall, and a long cable can deliver less voltage to the load.
A model can represent source resistance in series with the ideal source, then apply Ohm’s law to the complete network. The calculator’s single element does not include those hidden resistances unless they are entered explicitly.
AC circuits
For direct current and purely resistive steady-state circuits, V = IR uses real scalar values. Alternating-current circuits containing capacitance or inductance use impedance, a frequency-dependent complex quantity:
V = I × Z
Voltage and current can differ in phase. RMS values, waveform, frequency, real power, reactive power, and apparent power become relevant.
Entering an impedance magnitude as though it were resistance can give a current magnitude but loses phase information and should not be treated as a complete AC solution.
Tolerance and significant figures
A resistor marked 1 kΩ with 5% tolerance can lie within its specified band rather than equal exactly 1,000 Ω. Supply voltage, measurement accuracy, temperature, and connection resistance add uncertainty.
Long decimal output is useful for avoiding intermediate rounding but does not make components exact. Report results with precision appropriate to the least certain input and evaluate worst-case combinations when limits matter.
Safety limits
Ohm’s law can calculate a current that the source, conductor, switch, connector, resistor, or protective device cannot safely handle. It does not enforce insulation voltage, creepage, clearance, temperature rise, fault energy, or electric-shock requirements.
Mains and high-energy battery systems can cause lethal shock, fire, arc flash, and burns. Use applicable standards, protective equipment, isolation, qualified design, and competent supervision.
Limits of this calculator
The tool solves the ideal scalar relationship among one voltage, current, and resistance and reports corresponding power. It assumes the entered values describe the same operating point.
It does not model nonlinear behaviour, temperature, tolerance, source impedance, reactive components, transients, frequency, wiring, or protection. Negative values preserve a chosen sign convention but do not establish physical polarity automatically.
Use it to check arithmetic and simple DC resistor models. Use component data, circuit simulation, measurement, and applicable engineering standards for real design and safety decisions.