Series circuit rules
A series circuit has only one path for the current, so the current is the same through every part. The supply's voltage divides between the parts, each taking a share in proportion to its resistance.
IT = IR1 = IR2 = IR3 = …
RT = R1 + R2 + R3 + …
VT = VR1 + VR2 + VR3 + … (Kirchhoff's voltage law)
Switches, wires and connections that are working drop almost nothing: about 0 V across each.
Ohm's law
V = I × R I = V ÷ R R = V ÷ I
Use it for the whole circuit (VT, IT, RT) or for one part. A resistor's share of the supply is VR = IT × R.
Tolerance: close enough is normal
Real parts are never exact. A gold band on a resistor means it can be up to 5% off its color code, and a supply is a little off its setting too. A reading within about 5% of your calculation is normal. A reading far outside that points to a fault.
Fault symptoms
| Fault | Voltages, power on | Resistance, power off |
| An open: a resistor, a switch that will not close, a broken wire or connection | The whole VT across the open part, 0 V across every other part. No current flows anywhere. | OL across the open part |
| A short across a part | About 0 V across it. More than calculated across the others, and more current. | About 0 Ω |
| A resistor the wrong value (overheated: its resistance has risen) | More than calculated across it, less across the others, less current. | Far from its color code |
| A low supply | VT below the supply's rating, and every drop low by the same share. | Every part reads normal |
Two faults: an open anywhere still stops all the current, so it can hide a second fault. Two opens can each read 0 V on their own, because the other open is in series with the meter; measure across a span that contains both and the whole VT appears. After a repair, measure everything again: a second fault can show up only once the first is fixed.
Search smart
- Measure the source first. If VT is wrong, nothing else will be right.
- The walk. Put the black probe on the supply's − side (ground) and leave it there. Move the red probe from the + side along the circuit, one point at a time. Each reading is the voltage still left at that point, and it should step down a little at each resistor. A big step shows where most of the voltage is dropped; no step across a resistor means it is shorted, or no current is flowing.
- Split in half. Measure across half the circuit. If that half is wrong, the fault is in it. Split it again.
- Confirm before you replace. With the power off, check the part on Ω. Replacing a good part wastes time and money.
Repairing
- Replace only the parts your readings prove are bad.
- With the power on, measure the supply and every part again. Every reading should match your calculations. If one doesn't, the circuit is not fixed yet.
Measuring with a multimeter
- Voltage: black lead in COM, red in V Ω, dial on V⎓, power on. The probes go across the part, in parallel with it. Red on the side nearer the supply's + reads positive.
- Current: the meter has to be in series, so the current flows through it. Turn the power off, open the circuit (a switch turned off is a ready-made gap), move the red lead to A, turn to A⎓, and bridge the gap with the probes, red on the + side. Move the red lead back to V Ω when you finish. Across a part, an ammeter is a short.
- Resistance: power off, dial on Ω, probes across the part. An ohmmeter sends its own test current, so a powered circuit gives a meaningless reading. Anything wired straight to the supply stays live even with a switch off.
Significant figures
Match the precision of your least precise value: 12 V ÷ 470 Ω = 0.026 A (two significant figures, the same as 12). For a meter reading, write down exactly what the display shows.
Troubleshooting checklist
- Calculate what each reading should be: RT, IT, and the drop across each part.
- Measure VT, then search for the fault with as few readings as you can.
- Compare measured with calculated, and confirm on Ω with the power off.
- Diagnose: name the fault and the reading that proves it.
- Replace the bad part.
- Measure every part again to prove the repair worked.