How this instrument works
Series means one path and no branching: whatever current leaves your supply threads through every element in turn, with nowhere else to go. What differs from part to part is voltage. Each one claims a share of that drop in proportion to its own resistance, and Kirchhoff's loop rule insists those shares total supply voltage exactly. Because one shared current divides out of that sum, resistances themselves add — no reciprocals, no products, nothing to get backwards.
Addition of this kind sits inside Ohm's earliest published result. His 1826 measurements ran brass wires of eight different lengths through one circuit and fitted X = a ⁄ (b + x), where x stood for the length of wire he had added and b for everything else that current still had to cross — coil, contacts, measuring apparatus itself. That b + x is series addition in its first printed form, and it carries a lesson worth keeping: any long conductor simply is a queue of shorter ones, so resistance growing with length and resistance adding along a chain are one statement rather than two.
Plain addition assumes your listed parts are the entire path, which hardware contradicts in small ways that occasionally matter. Every solder joint, crimp, and breadboard spring donates its own milliohms, and here those strays inflate your total rather than diluting it — beneath notice beside a 10 kΩ chain, decisive once values fall to single ohms. Each entry is also taken as ohmic and thermally settled, so any part running hot drifts upward under its own dissipation. Above roughly fifty megahertz the lead inductance of each body adds along that path just as faithfully as resistance does, which is why one long string of small parts behaves worse than a single correct part.
- Put your first value into Resistor 1, switching its unit to ohms, kilohms, or megohms to match whatever is printed on that part.
- Enter your next into Resistor 2. Physical order along the path is irrelevant — chains total identically however you arrange them.
- Type a third value into Resistor 3 (0 if unused), or leave that field at zero when only two parts are involved.
- Read Total resistance. A sound answer is never smaller than your largest single entry.
- For chains longer than three, total your first three, put that sum back into Resistor 1, and carry on with whatever remains.
Worked example — 320 Ω from two drawer staples
A red LED on a 5 V rail, wanted at roughly 10 mA. The diode holds about 2.0 V by itself, so whatever resistance sits ahead of it must absorb 3.0 V, and 3.0 ⁄ 0.010 asks for 300 Ω. That value lives in E24; drawers stocked only to E12 jump from 270 straight to 330 with nothing between. So reach for two staples instead — enter 100 into Resistor 1, 220 into Resistor 2, and leave Resistor 3 (0 if unused) sitting at zero. Total resistance comes back as 320 Ω.
Those 320 Ω pass 3.0 ⁄ 320 = 9.375 mA, near enough to target that no eye could tell any difference. This pair also demonstrates how chains split voltage: 9.375 mA across 100 Ω drops 0.94 V, across 220 Ω drops 2.06 V, and those two sum to precisely 3.0 V — exactly what that diode left behind. Heat divides on identical proportions, near 8.8 mW in the smaller body against 19 mW in the larger, because one shared current makes dissipation track resistance. Along any chain it is your biggest value that runs hottest, an exact reverse of what happens between parallel branches.
Questions
Why do series resistances add when parallel ones do not?
Because chains share one current while parallel pairs share one voltage. With I common to every element, the drops I·R₁ + I·R₂ + I·R₃ have to equal I·R_total, and dividing that current out leaves plain addition standing. Parallel branches instead hold V in common, so it is their currents that add, which makes conductance rather than resistance your quantity to sum. Identical bookkeeping either way — what changes is which quantity every part is forced to share.
Which resistor in series runs hottest?
The largest one. Current is identical at every point along one path, so dissipation P = I²R climbs in direct proportion to resistance — 220 Ω sheds 2.2 times as much heat as 100 Ω sitting beside it. This catches people who have internalised parallel behaviour, where whichever branch is smallest hogs both current and heat. Sizing packages for chains, start with your biggest value and work down.
Should I leave that third field empty or type zero?
Type 0, which is exactly what the Resistor 3 (0 if unused) label asks for. Zero contributes nothing to any sum, so two-part chains compute correctly. Real hazard runs in reverse: one stale figure left in that box from an earlier calculation quietly inflates every total afterwards. If your result comes out larger than expected, check that third field before doubting your arithmetic.
Do tolerances add up as well?
Not in percentage terms, which tends to surprise people. Stack parts of matching tolerance and worst case holds at that same percentage — 320 Ω built from 1% parts is still 1%, since nominal sum and error sum scale together. Reality is usually tighter still, because two independent errors seldom peak in one direction at once. Mixing grades is what hurts: one 10% part swamps whatever precision sits next to it.
When does a small resistor stop mattering in series?
Roughly once it falls under one hundredth of your total, where it vanishes beneath the tolerance of everything around it. Drop 10 Ω into 100 kΩ of chain and you have moved your answer by 0.01%, far inside uncertainty of even 1% parts. Instinct here inverts from parallel wiring, where small values dominate and large ones are nearly invisible. Chains are governed by their biggest member, parallel pairs by their smallest.
Why stack resistors rather than buy one right value?
Three reasons that come up on real benches. Voltage rating is chief among them — high-voltage probes are stacks of ordinary parts precisely because each body withstands only some hundreds of volts, and chains spread that stress. Power rating scales identically, three packages sharing one current to shed heat that would cook any lone part. Then there is stock: E12 gives you 270 and 330 and nothing between, so 320 Ω arrives as 100 plus 220 or it does not arrive at all.