Skip to content
Brainlag

Ohm's law and circuits

Find voltage, current, resistance or power from any two with V = IR, and add up resistors in series and parallel, with the working shown. For GCSE and A-level physics.

See it happen: Series & parallel circuits

Learn this properly

Lessons from the Combined and Separate Science courses on this topic: worked steps, then exam-style questions with new numbers every time.

See the whole course

Formulas

Ohm's lawV = IR
PowerP = IV = I2R = V2 / R
SeriesR = R₁ + R₂ + R₃ + ...
Parallel1/R = 1/R₁ + 1/R₂ + 1/R₃ + ...

Worked example

A 12 V battery is connected to a 4 Ω and a 6 Ω resistor in parallel. Find the total resistance, the current from the battery and the power.

  1. 1/R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12, so R = 12/5 = 2.4 Ω.
  2. I = V / R = 12 / 2.4 = 5 A.
  3. P = IV = 5 × 12 = 60 W.

Answer: 2.4 Ω, 5 A and 60 W.

Common mistakes

  • Adding parallel resistors as if they were in series: the total in parallel is always less than the smallest resistor.
  • Forgetting the last step in parallel: 1/R = 5/12 means R = 12/5, not 5/12.
  • Ignoring prefixes: 250 mA is 0.25 A and 4.7 kΩ is 4700 Ω.
  • Using the voltage across one component with the resistance of a different one.

How it works

This circuit calculator has two parts. The Ohm's law tab takes any two of voltage, current, resistance and power and finds the other two, with the formula and the working. The Resistors tab adds up a list of resistors in series and in parallel. Unit prefixes such as mA, kΩ and kW are built in, so you can type values as they appear in the question.

  1. Ohm's law tab: enter any two of V, I, R and P and choose the unit for each, such as mA or kΩ.
  2. Read the two missing values with the formulas used: V = IR, P = VI, P = I2R or P = V2/R.
  3. Resistors tab: type each resistance in its own row. Add more rows with the add button and remove any you do not need.
  4. Read the total resistance in series and in parallel, with the working for both.
  5. Enter a supply voltage to see the current through the combination.

Tips

  • Watch the prefixes: 1 mA = 0.001 A and 1 kΩ = 1000 Ω. A 12 V supply across 4 kΩ gives 3 mA, not 3 A.
  • In series, resistances add: 2 Ω + 3 Ω = 5 Ω. In parallel, the reciprocals add: 1/R = 1/6 + 1/3 = 1/2, so 6 Ω and 3 Ω in parallel give 2 Ω.
  • The total resistance in parallel is always smaller than the smallest single resistor. If your answer is bigger, check the last step: you still need to flip 1/R.
  • With 12 V across 4 Ω, the current is 3 A and the power is 36 W. VI, I2R and V2/R all give the same 36 W, which makes a quick check.

FAQ

Does every component obey Ohm's law?
No. Ohm's law holds for ohmic conductors, such as a fixed resistor at constant temperature, where the current is proportional to the voltage. A filament lamp heats up and its resistance rises, and a diode lets current through in one direction only, so neither follows it. V = IR still gives the resistance at any one moment.
Which two values do I need?
Any two of V, I, R and P. Every pair is enough to find the other two, because the formulas link all four. The working shows which formula was used for each answer.
Which unit prefixes can I use?
Voltage in mV, V or kV, current in µA, mA or A, resistance in Ω, kΩ or MΩ, and power in mW, W or kW. The working converts everything to base units first.
How is the current found in the Resistors tab?
The calculator divides the voltage you enter by the total resistance of the combination, using I = V / R.

Keep going

Printables