The top row is the basic relation: drag the voltage and resistance sliders and the current and the power follow. The lower row compares 4Ω and 6Ω wired in series and in parallel. Series comes to 10Ω, parallel to 2.4Ω.
How to read this board
There is only one formula here: current = voltage ÷ resistance. Fix any two
of the three and the third is fixed too, which is why two sliders and one calculation card
are enough.
The lower row exists because the two wirings do not share a formula.
Series is 4 + 6. Parallel is 1 ÷ (1/4 + 1/6). The same word
"connect", one an addition and the other a reciprocal.
Where it trips you up
The places that are easy to get wrong, next to how to check each one on the board.
| Where it trips you up | Why that happens | How the board shows it |
|---|---|---|
| Parallel lowers the resistance | It feels like adding resistance should add resistance. What is actually being added is another path for the current. | 4Ω and 6Ω in parallel come to 2.4Ω, below either of them. Parallel always does this. |
| The reciprocal formula will not stick | 1/R = 1/R1 + 1/R2 does not look like the other formulas. | The board writes 1 / (1/4 + 1/6) out in full, so the procedure can be followed from the formula itself. |
| How the total current differs between the two | Since current = voltage ÷ resistance, at the same voltage a smaller combined resistance draws more current from the supply. |
Fix the voltage at 12V: series is 10Ω for 1.2A, parallel is 2.4Ω for 5A. Comparing bulb brightness, though, needs the power in each bulb rather than the total current. |
| Power and current get confused | Both sound like "a lot is flowing". Power is voltage × current. | The power card is on the board. Hold the voltage and change the resistance: the power changes too. |
| Taking the resistance towards zero | On this formula alone, the smaller the resistance the larger the current, without limit. Real circuits have resistance in the supply and the wiring, but a short circuit still draws a very large current, with heat and damage following. | Drag the resistance slider to its minimum and watch the current jump. The formula has no safety device in it. |
| Household sockets, series or parallel | In series, one failure would take everything out. They are parallel. | A smaller combined resistance means more current — which is the same reason a breaker trips. |
Resistance measures how hard it is for current to get through, so more routes make it easier. Series lengthens the route and makes it harder; parallel adds routes and makes it easier. The reciprocal of resistance can be treated as how easily current passes, and in parallel those add — which is why the combined resistance always comes out below every resistor in it.
Try this
- Halve the resistance — the current doubles. At a fixed voltage the two are inversely proportional.
- Make both resistors equal — the parallel combination lands on exactly half. Two identical routes, twice the ease.
- Make resistor 2 very large — the parallel total closes in on resistor 1. A route that is hard enough barely gets used.