Ohm's Law: Relating Voltage, Current, and Resistance in Series and Parallel Circuits

Concept

The last lesson defined voltage, current, and resistance as three separate quantities — electrical pressure, the flow of charge, and the opposition that flow runs into. Ohm's Law is the single relationship that ties all three together, and once it's understood as one idea rather than three formulas to memorize, most of the arithmetic in this unit stops being intimidating. Stated one way: voltage equals current multiplied by resistance — push harder (more voltage) and the same resistance lets more current through; add resistance and the same voltage pushes less current through. That's the whole idea, and it holds regardless of which quantity happens to be the unknown one. If voltage and resistance are both known but current isn't, ordinary algebra rearranges that same relationship to solve for current instead: divide voltage by resistance. If voltage and current are both known but resistance isn't, the same rearrangement solves for resistance: divide voltage by current. Nothing new is being learned in either rearrangement — it's the identical relationship, just isolated for whichever letter happens to be missing in a given problem. Written with the standard shorthand — E for voltage in volts, I for current in amps, R for resistance in ohms — the three faces of the same idea are E = I × R, I = E ÷ R, and R = E ÷ I. A lot of learners try to memorize all three side by side as if they were unrelated; that's more work than necessary and more fragile besides, because a forgotten formula is just gone, while a relationship that's actually understood can always be re-derived from the other two forms in a few seconds.

Concept

Try it with numbers that aren't from any exam question. A 6-volt battery pushes current through a 3-ohm resistor. Voltage and resistance are both known, current isn't, so reach for the current version of the relationship: divide voltage by resistance, 6 divided by 3, and the answer is 2 amps. Same relationship, different missing piece: that same 6-volt battery, now known to be pushing 2 amps, connects instead to some resistor whose value isn't given — divide voltage by current, 6 divided by 2, and the resistor turns out to be 3 ohms again, which makes sense, since it's the same numbers running the other direction. The one place this trips people up on the exam has nothing to do with the algebra and everything to do with units: volts, amps, and ohms are the base units the relationship actually runs on, and a value quietly given in milliamps or kilohms has to be converted back to amps and ohms before Ohm's Law will produce a correct answer. That conversion is worth its own lesson coming up next in this unit, but it's worth flagging here, because a perfectly correct application of Ohm's Law to un-converted units still hands back a wrong number — the arithmetic isn't broken, the units feeding into it are.

Concept

Circuits come in two basic shapes, and which shape a circuit takes changes which quantity stays constant across every component in it. A series circuit gives current exactly one path to follow — every component sits along that same single loop, one after another, with no branch point anywhere for current to split off onto a different route. Because there's only one path, the same current has to be flowing through every component in that loop at every instant; measure it anywhere along a series circuit and the reading comes out identical, no matter which component the meter sits next to. What does change from one component to the next is voltage: each resistor in the series string drops some share of the total voltage as current pushes through it, and a resistor with more resistance claims a bigger share of that total than one with less. Add up the individual voltage drops across every component in a series loop and the sum always comes back to the full voltage the source is supplying — none of it goes missing, it's just divided up unevenly across whatever stands in the current's one and only path.

Concept

A parallel circuit is built the opposite way: instead of one path, it offers current several separate branches, all connected across the very same two points. Because every branch shares those same two connection points, every branch sees the exact same voltage across it — that's the one quantity a parallel circuit holds constant, mirroring exactly what a series circuit holds constant for current. What varies branch to branch is current: a branch with less resistance lets more current flow through it for that shared voltage, a branch with more resistance lets less through, and the total current the source has to supply is the sum of whatever each individual branch is drawing on its own. That's a direct mirror image of the series case: series holds current constant and splits voltage up; parallel holds voltage constant and splits current up. Keeping both pictures side by side — one path versus several, constant current versus constant voltage — is usually enough to stop the two shapes from blurring together under exam pressure.

Concept

These aren't abstract shapes drawn on a whiteboard — a station is full of both, and knowing which is which explains behavior that would otherwise seem mysterious. Wire a string of components in series and a single failure anywhere along that one path breaks the entire loop, because there was never more than one route for current to take in the first place — exactly the old style of holiday lights where one dead bulb darkened the whole string. Wire the same components in parallel instead and a failure in one branch leaves every other branch completely unaffected, since each branch keeps its own independent connection across the same two points, which is why household and station wiring runs parallel rather than series: a failed lamp or a failed radio shouldn't be able to take the rest of the circuit down with it. The same reasoning is why battery packs get wired one way to add up voltage and a different way to add up current capacity at the same voltage — a distinction worth having settled in advance, well before it becomes relevant to a specific piece of gear on the bench.