Ohm's law tells you what ONE resistor does. Kirchhoff's two laws tell you what a whole network does, and every technique later in this chapter — Thevenin, Norton, delta-wye — is built out of them. The first is the loop rule, and it is conservation of energy wearing an electrician's coat.

Set off from any point in a closed loop and walk all the way round it. Every source you pass hands you volts; every element you pass through takes some back. Arrive where you started and you must be at exactly the potential you left at — so the gains and the losses cancel. For a source feeding three elements in series that reads $V_s = V_1 + V_2 + V_3$ — V-s equals V-one plus V-two plus V-three. $V_s$ is the source voltage in volts, the EMF driving the loop; $V_1$, $V_2$ and $V_3$ are the drops across the first, second and third element, also in volts, and the subscripts are nothing but the order you meet them walking round. Solve it forwards for the source, or backwards for whichever drop you could not reach with a probe.

The sign discipline is the physics, so say it out loud once: walking through an element in the direction of the current is a DROP, and a drop subtracts; walking through a source from minus to plus is a RISE, and a rise adds. Write it as “everything sums to zero” and the signs do the bookkeeping for you. Write it as “source equals the sum of the drops” and you have already done the signs in your head — which is fine, provided you meant to.

One nugget for the lab: this is why a broken element in a series string reads the FULL supply voltage across the break. Everything else in the loop has stopped dropping anything, so the loop hands the whole lot to the one gap. A meter across a blown element showing the rail is not a fault in the meter.