Resistors combine differently in series (they add) and parallel (the reciprocals add). Drag the sliders below to set the battery voltage and three resistors, flip the series/parallel toggle, and watch the total resistance and current respond in real time.

One Toggle Sends Three Resistors From a Sum to Below the Smallest

Leave Resistor R1, R2, R3 untouched and flip only the SERIES/PARALLEL switch: the same three components report a completely different total resistance. In series the readout sums them, R_total = R1 + R2 + R3, a value larger than any single resistor, and the total current falls. In parallel the sim computes the reciprocal-sum, 1/R = 1/R1 + 1/R2 + 1/R3, landing below even your smallest resistor, so the current climbs. Nothing about the parts changed — only how they connect between the two battery terminals.

Watch the per-resistor panels to see why. Wired in one line, the same current threads every resistor and the Battery voltage divides, with the biggest resistor claiming the largest share. Wired side by side, the same voltage sits across each branch and the current splits instead, more of it slipping through the smaller resistance. That side-by-side wiring hides the classic trap: giving the current several paths at once lowers the total resistance and raises the total current — in parallel, more paths mean less resistance, not more.

It is the difference between old fairy lights, where one dead bulb in series darkens the whole string, and house sockets in parallel, each handed full mains voltage. Pin down the arithmetic on the resistor calculator, then keep testing circuits and fields across our library of interactive simulations.

Frequently asked questions

How do you add resistors in series?

In series the resistances simply add: R_total = R1 + R2 + R3. The total is larger than any single resistor, the same current flows through all of them, and the voltage divides between them.

How do you add resistors in parallel?

In parallel the reciprocals add: 1/R_total = 1/R1 + 1/R2 + 1/R3. The total resistance is smaller than the smallest branch, every branch has the same voltage, and the current divides between them.

Does adding a resistor in parallel increase the resistance?

No — it decreases it. Wiring resistors side by side gives the current more paths, so the total resistance drops below the smallest branch and the total current rises. More resistors mean more resistance only in series.

What is the difference between series and parallel current?

In series the same current passes through every component, because there is only one path. In parallel the current splits between the branches, with more of it flowing through the smaller resistance.

References & formula source

  • Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 27 (Circuits), resistors in series and parallel.
  • Young & Freedman — University Physics with Modern Physics, §26.1 (Resistors in Series and Parallel).
  • R. Nave — HyperPhysics, Georgia State University, "Resistor Combinations" section.