Physics
Ohm's law calculator
Ohm's law with the formula reversed at will: leave blank the quantity you want — voltage, current or resistance — and the calculation adapts. Plus resistors in series and in parallel, with the read-out for each component.
Ohm's law and the two ways to connect resistors
Ohm's law says that in a conductor the current is proportional to the applied voltage: V = R·I. The resistance R is the constant of proportionality and is measured in ohms. It is not a universal law but a property of certain materials, called ohmic: a diode or an incandescent bulb does not obey it, because its resistance changes with current and temperature.
In series the resistors carry the same current, since there is no alternative path, and the voltages across them add up to the supply voltage. The equivalent resistance is therefore the sum, and is always greater than the largest one. In parallel it is the opposite: every resistor sees the same voltage and each draws its own current, so the currents add and the equivalent resistance is always smaller than the smallest one.
The power dissipated, P = V·I, is the quantity that decides whether a component survives. Its equivalent forms P = R·I² and P = V²/R follow by substituting Ohm's law, and are useful when you do not know both quantities. It is the number to compare with a resistor's rated power before fitting it.
Common mistakes
- Adding resistances in parallel as well: in parallel you add the reciprocals, and the result is smaller than any single resistance. If your parallel comes out larger than one component, you used the series formula.
- Treating milliamperes as amperes: 250 mA is 0.25 A, and forgetting the conversion throws the answer off by a thousand.
- Applying Ohm's law to non-ohmic components: for LEDs, diodes and bulbs the resistance is not constant, and the V/I ratio computed at one point does not hold at the others.
Frequently asked questions
What is the formula for Ohm's law?
V = R·I, so I = V/R and R = V/I. Voltage is measured in volts, current in amperes and resistance in ohms.
How do you calculate equivalent resistance in parallel?
Add the reciprocals and invert the result: 1/Req = 1/R₁ + 1/R₂ + … For just two resistors there is the shortcut Req = (R₁·R₂)/(R₁+R₂). The value is always smaller than the smallest resistance in the group.
How do you calculate the power dissipated by a resistor?
P = V·I, or P = R·I² if you know current and resistance, or P = V²/R if you know voltage and resistance. These are three ways of writing the same quantity, obtained by substituting Ohm's law.
Why is the current the same everywhere in a series circuit?
Because charge does not pile up anywhere and there are no alternative paths: everything that enters a resistor must leave it. What changes along the series is the voltage, which divides in proportion to the resistances.
How this calculation works
Ohm's law: V = R·I, I = V/R, R = V/I. Power dissipated: P = V·I = R·I² = V²/R. Resistors in series: Req = R₁ + R₂ + … + Rₙ; the current is common and the voltage across each is Vᵢ = I·Rᵢ (voltage divider). Resistors in parallel: 1/Req = 1/R₁ + 1/R₂ + … + 1/Rₙ; the voltage is common and the current in each branch is Iᵢ = V/Rᵢ (current divider). For two resistors in parallel: Req = (R₁·R₂)/(R₁ + R₂).
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