How do you add resistors in series and in parallel?

In series they add, R = R₁ + R₂. In parallel the reciprocals add, 1/R = 1/R₁ + 1/R₂, so the total is smaller than the smallest resistor.

Why do parallel circuits draw more current?

Each branch is another path for charge, so the total resistance drops. With the same battery voltage, I = V/R goes up.

What is internal resistance?

A real battery has some resistance inside it. When current flows, part of the EMF is used up inside, so the terminal voltage is V = ε − Ir.

What resistor do I add in parallel to get a given total?

Rearrange 1/R = 1/R₁ + 1/R₂ to R₂ = R₁R/(R₁ − R). To bring a 20 Ω resistor down to 12 Ω, add R₂ = 20 × 12 / (20 − 12) = 30 Ω in parallel. The target must be below 20 Ω, because parallel always lowers the total. Pick Parallel R₂ for a total under Solve for to see each step.

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Series & parallel circuits

Ohm's law in action: watch the current respond as you change voltage, resistance and wiring.

Just need the number? Ohm's Law and Circuits

Current vs voltage

Readouts

What's happening

Current is voltage divided by total resistance. In series the resistances add, so each added resistor slows the whole loop. In parallel each resistor offers its own path, total resistance drops, and the battery drives more current. The moving dots pace with the actual current; the graph shows the I–V line whose slope is 1/R.

I = V / RR = R₁ + R₂1/R = 1/R₁ + 1/R₂

GCSE Physics (AQA 4.2.2, Edexcel, OCR): series and parallel circuits, Ohm's law and power. A-Level Physics: internal resistance and terminal voltage.

Challenge

Predict first: with R₁ = R₂, is the parallel current twice, four times, or half the series current at the same voltage? Work it out, then flip the toggle.

FAQ

How do you add resistors in series and in parallel?: In series they add, R = R₁ + R₂. In parallel the reciprocals add, 1/R = 1/R₁ + 1/R₂, so the total is smaller than the smallest resistor.
Why do parallel circuits draw more current?: Each branch is another path for charge, so the total resistance drops. With the same battery voltage, I = V/R goes up.
What is internal resistance?: A real battery has some resistance inside it. When current flows, part of the EMF is used up inside, so the terminal voltage is V = ε − Ir.
What resistor do I add in parallel to get a given total?: Rearrange 1/R = 1/R₁ + 1/R₂ to R₂ = R₁R/(R₁ − R). To bring a 20 Ω resistor down to 12 Ω, add R₂ = 20 × 12 / (20 − 12) = 30 Ω in parallel. The target must be below 20 Ω, because parallel always lowers the total. Pick Parallel R₂ for a total under Solve for to see each step.