/* chapter2.jsx — Chapter 2: Series & Parallel
Same scrollytelling structure as chapter 1, with topology-switching visuals.
Helpers (fmt, useInViewCallback, Slider, ProgressBar, TopBar, ChapterNav,
CommonTweaks, useCrossChapterPersistence) come from shared.jsx via window. */
const { useState, useEffect, useRef } = React;
/* ─── Beats ─────────────────────────────────────────────────────────────── */
function BigIdeaBeat({ onView, kids }) {
const ref = useInViewCallback(onView);
return (
§ 02 · the two shapes
{kids ? (
<>
Same parts. Different shape.
Imagine two pinches in a pipe. You can put them one after
the other, or side by side. The flow turns out
very different.
) : (
<>
Same parts, different shape.
Take two resistors. You can string them like beads on a thread —
series. Or branch them like a fork in the road —
parallel. The math is different, and the behavior is wildly different.
)}
Series adds up. Parallel splits apart.
Series · one road
Same flow. Different push at each pinch.
Resistances add: R = R₁ + R₂
Parallel · two roads
Same push. Different flow in each branch.
Currents add: I = I₁ + I₂
a note on labels
{kids
? <>From here on you'll see little numbers, like R₁ and R₂. When there are two of the same part, we give each a tiny number to tell them apart — R₁ is the first pinch, R₂ the second. The flow through each gets a matching tag: I₁, I₂. That's all the little number means — a name tag.
: <>One quick convention before we dig in: when a circuit has more than one of the same part, we tag each with a small subscript number. R₁ and R₂ are simply the first and second resistor; I₁ and I₂ are the current flowing through each. Nothing mathematical — just a way to keep two of the same thing straight.}
{!kids && (
Real circuits mix and match. We'll learn both rules and use them
for the rest of the series.
)}
);
}
function SeriesBeat({ v, r1, r2, setR1, setR2, onView, kids }) {
const ref = useInViewCallback(onView);
const I = v / (r1 + r2);
return (
§ 03 · one road · series
SERIES
One pipe. Two pinches.
{kids ? (
<>
Put two pinches in the same pipe, one after the other. The
water has to squeeze through both.
All the water goes through all the pinches — so the flow is the same
everywhere. Right now it's {fmt(I, 2)} A.
Each pinch uses up a little of the push as the water squeezes
through. So the barrel's push gets shared between the two
pinches — by the end of the pipe, it's all been spent.
Tighten either pinch and the whole flow slows down.
) : (
<>
Drop two resistors into a single loop, one after another — two
pinches in the same pipe.
Picture the water reaching the first pinch, squeezing through, then
running straight into the second. Whatever gets through one must get through the other — there's nowhere else to go, and
water can't pile up in the pipe. So the flow is identical at
every point in the loop.
But each pinch costs push. The water spends some of its
pressure forcing through the first narrowing, then more through the
second — and by the time it loops back, the whole push has been used
up, divided between the two. Two narrowings in a row are also harder
to pass than either one alone, so the shared flow runs slower than it would with a single pinch.
Put plainly: the resistances simply add.
Rtotal=R1+R2
And the flow follows Ohm's law as before, just with the bigger total
resistance:
I=VR₁ + R₂={fmt(I, 2)}A
)}
try it · adjust each pinch
same flow everywhereI = {fmt(v,1)}V ÷ ({fmt(r1,1)}+{fmt(r2,1)})Ω = {fmt(I, 2)} A
{!kids && (
push used at each pinchV₁ = {fmt(I*r1,1)}V · V₂ = {fmt(I*r2,1)}V (adds to {fmt(v,1)}V)
)}
{kids
? "See the water level step down at each pinch? That's the push being used up. The bulb is dim if either pinch is tight — both pinches matter."
: <>Each resistor uses up — “drops” — part of the push; the two drops always add back to the full {fmt(v,1)} V. Watch the water level in the pipe step down at each pinch (the % push left labels) — the bigger pinch takes the bigger step. The flow itself stays the same all the way round.}
{kids ? "why it's called a “drop”" : "why engineers say a resistor “drops” voltage"}
{kids
? <>Think of the pinches as waterfalls. In series, one stream tumbles over two falls in a row — the two falls stack up to the whole cliff.
: <>Make height literal: voltage is the cliff. In series one stream goes over two falls in a row — same stream (same I), and the two fall heights stack to the full cliff. Your sliders move the ledge.}
{kids ? "the rule to remember" : "rule of thumb"}
{kids
? <>More pinch = less flow. Every time. Tighten either pinch and the whole loop slows down.
: <>In series, every ohm you add slows the whole loop: resistance up → current down. Drag either slider up and watch I fall — it never goes the other way.}
Now split the pipe into two. Each branch has its own pinch and its
own flow.
Each branch gets the full push from the barrel — they don't
share. Right now branch 1 has {fmt(I1, 2)} A,
branch 2 has {fmt(I2, 2)} A,
and the total coming out is {fmt(Itot, 2)} A.
If you close one branch (huge pinch), the other branch keeps
going. Pretty clever, right?
) : (
<>
Now fork the pipe: the water reaches a junction and can take either branch.
Both branches start and end at the same two points, so each one
feels the same full pressure from the barrel — they don't
share the push the way two pinches in a line do. What differs is the flow: a loose branch lets plenty through, a tight one only a
trickle. Add up what each branch carries and you get the total
leaving the barrel — so the currents add:
Itotal=I1+I2=VR₁+VR₂
Here's the twist — opening a second branch doesn't change the first
one at all, yet more total water now flows. More lanes means
easier passage, so the combined resistance is less than
either branch alone:
1Rtotal=1R₁+1R₂
For two resistors this is the same as the tidy
R = (R₁·R₂) ÷ (R₁+R₂) shortcut you'll see in
the rules below — just rearranged.
If a branch opens (a bulb burns out), only that branch dies. The
others keep going. This is why your house's lights are wired in
parallel — and why old-style Christmas lights, wired in series,{" "}
all went dark when one bulb died.
)}
{kids ? "the waterfall, again" : "the waterfall picture, flipped"}
{kids
? <>Now the two falls sit side by side off the same cliff. Each one falls the whole way down — and the two streams add up.
: <>Same cliff, two spouts. Each branch falls the full height (full V across each) — what adds now is the water, not the height. Series stacks falls; parallel stacks streams.}
{kids ? "add the branches" : "total current, live"}
Itotal={fmt(I1, 2)}+{fmt(I2, 2)}={fmt(Itot, 2)}A
{kids ? "Both branches pour into the same exit — so their flows add up."
: "Each branch's current adds into the shared return path. Change either R and watch the total track it."}
{kids ? "the rule to remember" : "rule of thumb"}
{kids
? <>Inside each branch it's the same old rule — more pinch, less flow. But adding a branch is a new road for the water, so the total flow goes UP!
: <>Within any one branch, the rule holds: resistance up → current down. But adding a branch lowers the total resistance — more roads → more total flow. Same law, opposite feel.}
Same battery, same two resistors. Wired one way vs. the other.
What does your gut say?
);
}
function RulesBeat({ v, r1, r2, onView, kids }) {
const ref = useInViewCallback(onView);
const I_s = v / (r1 + r2);
const I_p = v / r1 + v / r2;
if (kids) {
return (
§ 05 · two rules to remember
Two rules, and you're done.
Both shapes use the same V, I, and R from Chapter 1. Just two new
rules tell you how things combine.
Series · one road
Same flow through everything.
Push splits up across the pinches.
Squeezes add.
Parallel · two roads
Same push across each branch.
Flow splits up between branches.
Flows add.
same V & Rs · different totals
With {fmt(v, 1)} V,
R₁={fmt(r1, 1)}Ω, R₂={fmt(r2, 1)}Ω:
Series total flow: {fmt(I_s, 2)} A Parallel total flow: {fmt(I_p, 2)} A
Same parts. Way different result.
);
}
return (
§ 05 · the rules
Two shapes, two rules.
These two relationships will follow you through every circuit you ever
analyze. Memorize them once — they don't change.
Series
R=R₁+R₂
Resistances add. Same current everywhere. Voltage divides
across each resistor in proportion to its R.
Parallel
1R=1R₁+1R₂
Currents add. Same voltage across each branch. Total resistance
is less than the smallest single branch.
handy shortcut · two resistors
R=R₁ · R₂R₁ + R₂
Same rule as above, just solved for R — and only for two resistors at
a time. Two equal ones → exactly half:
6 Ω ∥ 6 Ω = 36 ÷ 12 = 3 Ω.
same parts, different totals
series:{fmt(I_s, 2)}A·parallel:{fmt(I_p, 2)}A
V = {fmt(v, 1)} V, R₁ = {fmt(r1, 1)} Ω, R₂ = {fmt(r2, 1)} Ω. Same components,
dramatically different flow.
);
}
function PlaygroundBeat({ v, setV, r1, setR1, r2, setR2, topology, setTopology, onView, kids }) {
const ref = useInViewCallback(onView);
const I_s = v / (r1 + r2);
const I_p = v / r1 + v / r2;
const I = topology === "series" ? I_s : I_p;
const tone = useToneFollow();
const idle = React.useRef(null);
// hear the current — parallel will sing higher than series for the same parts
const sing = (nv, nr1, nr2, topo) => {
const cur = topo === "series" ? nv / (nr1 + nr2) : nv / nr1 + nv / nr2;
tone.set(Math.min(1, cur / 24), Math.min(1, cur / 12));
if (idle.current) clearTimeout(idle.current);
idle.current = setTimeout(() => tone.stop(), 300);
};
const onV = (x) => { setV(x); sing(x, r1, r2, topology); };
const onR1 = (x) => { setR1(x); sing(v, x, r2, topology); };
const onR2 = (x) => { setR2(x); sing(v, r1, x, topology); };
const onTopo = (t) => { setTopology(t); sing(v, r1, r2, t); };
return (
§ 06 · all knobs unlocked
Pick your shape.
{kids
? <>Flip between the two and see what happens. Same parts. Different shape.
: <>Toggle topology, drag the sliders. The visualizations on the right reconfigure.
}
WATER · {topology === "series" ? "two pinches in line" : "two branches in parallel"}
{topology === "series"
?
: }
{showCircuit && (
THE LOOP · {topology === "series" ? "charge through two pinches" : "charge splits, then rejoins"}
)}
);
}
/* ─── LessonScrollyteller ─────────────────────────────────────────────── */
/* readout strip under a section's visual — computed for that section's topology */
function VisReadout({ v, r1, r2, topology, kids }) {
const Itot = topology === "series" ? v / (r1 + r2) : (v / r1 + v / r2);
const Req = topology === "series" ? (r1 + r2) : (r1 * r2) / (r1 + r2);
const P = v * Itot;
return (
{kids ? "Push" : "Voltage"}{fmt(v, 1)}V
{topology === "series" ? "R total · series" : "R total · parallel"}{fmt(Req, 1)}Ω
{kids ? "Flow" : "Total I"}{fmt(Itot, 2)}A
Power{fmt(P, 1)}W
);
}
/* ─── LessonScrollyteller ─────────────────────────────────────────────────
Restructured: each interactive section owns its OWN sticky visual, fixed to
that section's topology. No scroll-driven topology guessing — the diagram is
always physically beside the text it illustrates. */
function LessonScrollyteller({ showCircuit, kids }) {
const [v, setV] = useState(9);
const [r1, setR1] = useState(3);
const [r2, setR2] = useState(6);
const [topology, setTopology] = useState("series"); // Playground only (user toggle)
const [mode, setMode] = useState("cover"); // nav highlight only
const visHeight = showCircuit ? 330 : 530;
const stickyFor = (topo) => (
);
return (
{/* Big idea — full-width intro, no visual */}
setMode("map")} kids={kids} />
{/* SERIES — its own series-only visual */}
setMode("series")} kids={kids} />
{stickyFor("series")}
{/* PARALLEL — its own parallel-only visual */}
setMode("parallel")} kids={kids} />
{stickyFor("parallel")}
{/* Predict + Rules — full-width text */}
setMode("predict")} kids={kids} />
setMode("rules")} kids={kids} />
{/* Playground — the ONE place topology switches, and the user drives it */}
setMode("playground")} kids={kids} />
{stickyFor(topology)}
);
}
/* ─── Worked example: Christmas lights ────────────────────────────────── */
function PotDividerSection({ kids }) {
return (
§ 08 · the knob · an adjustable pinch
{kids ? <>The knob that turns the squeeze. : <>Meet the knob: the adjustable resistor.}
{kids
? <>Every volume dial, dimmer, and joystick hides the same part: a potentiometer. It’s just a pinch you can change by turning a knob — the very slider you’ve been dragging this whole time, made real. Turn it one way, more flow (brighter). Turn it back, less flow (dimmer).
: <>Every volume dial, dimmer, and joystick is the same part — a potentiometer: a resistor whose value you set by turning a knob. It’s the resistance slider you’ve been dragging, made physical. Wired across the supply, its middle tap (the wiper) is an adjustable voltage divider — dial any fraction of the voltage you like.}
{kids
? <>Try it: open The Workbench, load the “Dimmer” example, and drag the knob to fade the light up and down.
: <>Try it hands-on: in The Workbench (Lights bench) load the “Dimmer” example and drag the knob — watch the LED current, brightness, and the charge flow respond in real time.}
);
}
function WorkedExampleSection({ kids }) {
if (kids) return null;
return (
§ 07 · why Christmas lights die together
A practical story: Christmas lights.
Old strings of Christmas lights were wired in series.
Twenty tiny bulbs, end-to-end, plugged into a wall outlet. They
worked beautifully — until one bulb burned out.
All of them went dark. The series loop was broken; current
had no way to flow through the surviving bulbs. You had to test
every single bulb to find the dead one.
Modern strings (and your house's lights) wire each bulb in{" "}
parallel. One bulb dies, its branch opens, but the
other branches keep their own voltage and keep glowing.
series voltage budget
20 bulbs, 120 V outlet. Each bulb drops:
Vbulb = 120 V / 20 = 6 V each
parallel voltage budget
Each bulb wired across the full 120 V outlet. Each gets:
Vbulb = 120 V
That's why parallel bulbs are physically bigger — they're built
to handle the full line voltage.
the trade-off
Series: cheap, but fragile. Parallel: robust, but each part
needs to handle full voltage. Engineering is choosing.
);
}
/* ─── Quiz banks ──────────────────────────────────────────────────────── */
const ADULT_QUIZ = [
{
q: "Two resistors in SERIES. How does the total resistance compare to each one?", kind: "concept",
options: ["Larger than either", "Smaller than either", "Equal to the bigger one", "Always zero"],
correct: 0,
explain: "In series, resistances add: R = R₁ + R₂. The total is always bigger than either part.",
},
{
q: "Two resistors in PARALLEL. The total resistance is…", kind: "concept",
options: ["Larger than either", "Smaller than either", "The average of the two", "Always 1 Ω"],
correct: 1,
explain: "More paths means easier flow. Parallel total is always less than the smallest branch.",
},
{
q: "In a series loop, the current through R₁ versus R₂ is…", kind: "concept",
options: ["Bigger through R₁", "Bigger through R₂", "The same through both", "Zero through both"],
correct: 2,
explain: "One path, one current. The same current flows through everything in a series loop.",
},
{
q: "Two 6 Ω resistors in parallel give a total resistance of…", kind: "math",
options: ["12 Ω", "6 Ω", "3 Ω", "0 Ω"],
correct: 2,
explain: "Equal parallel resistors halve: 6 Ω ∥ 6 Ω = 3 Ω.",
},
{
q: "Why did old series-wired Christmas lights all die when one bulb failed?", kind: "concept",
options: [
"The others overheated",
"One open break stops the single shared current path",
"The voltage doubled",
"They were never really in series",
],
correct: 1,
explain: "A series loop has one path. Break it anywhere and current stops everywhere.",
},
{
q: "Three 3 Ω resistors in series total…", kind: "math",
options: ["1 Ω", "3 Ω", "9 Ω", "27 Ω"],
correct: 2,
explain: "Series adds: 3 + 3 + 3 = 9 Ω.",
},
{
q: "In a parallel circuit, the voltage across each branch is…", kind: "concept",
options: ["split between them", "the same full voltage for each", "always zero", "doubled"],
correct: 1,
explain: "Each parallel branch sees the full source voltage — that's the defining feature.",
},
{
q: "A 2 Ω and a 4 Ω resistor in parallel. Using product-over-sum, the total is…", kind: "math",
options: ["6 Ω", "3 Ω", "1.33 Ω", "8 Ω"],
correct: 2,
explain: "(R₁·R₂)/(R₁+R₂) = (2·4)/(2+4) = 8/6 ≈ 1.33 Ω — less than the smaller branch (2 Ω).",
},
{
q: "9 V across two parallel branches, R₁ = 3 Ω and R₂ = 9 Ω. The TOTAL current is…", kind: "math",
options: ["1 A", "3 A", "4 A", "0.75 A"],
correct: 2,
explain: "I₁ = 9/3 = 3 A, I₂ = 9/9 = 1 A. Currents add: I_total = 3 + 1 = 4 A.",
},
{
q: "In a series loop, which resistor takes the bigger share of the voltage?",
kind: "concept",
options: ["The smaller resistance", "The bigger resistance", "They always split it evenly", "Whichever is closer to the battery"],
correct: 1,
explain: "Voltage divides in proportion to R — the bigger pinch takes the bigger step. (Same current through both, so V = I·R is larger where R is larger.)",
},
{
q: "You open a SECOND parallel branch. What happens to the current in the first branch?",
kind: "concept",
options: ["It drops by half", "It doubles", "It doesn't change — but the total from the battery goes up", "It stops"],
correct: 2,
explain: "Each branch sees the full source voltage independently. Adding a branch doesn't touch the first one — it just adds its own current to the total.",
},
{
q: "In a series pipe, whatever flows through the first pinch must also flow through the second, because…",
kind: "concept",
options: ["the pinches are identical", "water can't pile up or escape — there's only one path", "the second pinch pulls harder", "pressure is zero between them"],
correct: 1,
explain: "One path, nowhere to accumulate: the flow that gets through one pinch has no choice but to continue through the next. That's WHY series current is the same everywhere.",
},
{
q: "A volume dial or light dimmer is, underneath, a…",
kind: "concept",
options: ["tiny battery", "capacitor", "potentiometer — a resistor you adjust with a knob", "coil of wire"],
correct: 2,
explain: "A potentiometer is the resistance slider made physical: turn the knob, change R, change the flow.",
},
{
q: "The practical trade-off between the two wirings is…",
kind: "concept",
options: [
"series is robust, parallel is fragile",
"series is cheap but one failure kills all; parallel keeps parts independent but each must handle full voltage",
"parallel uses less wire and less power",
"there is no practical difference",
],
correct: 1,
explain: "Series: one shared path, cheap, fragile. Parallel: independent branches, robust — but every branch sees the full source voltage and must be built for it.",
},
];
const KIDS_QUIZ = [
{
q: "Two pinches in the SAME pipe, one after the other. The water has to…", kind: "concept",
options: ["pick just one", "squeeze through both", "skip them both", "go faster"],
correct: 1,
explain: "In a row (series), the water crosses both pinches — so both slow it down.",
},
{
q: "Splitting the pipe into TWO branches (parallel) means…", kind: "concept",
options: ["less total water gets through", "more total water gets through", "the water stops", "the water freezes"],
correct: 1,
explain: "Two roads instead of one! More ways through means more total flow.",
},
{
q: "In a single loop (series), the flow is…", kind: "concept",
options: ["different in different spots", "the same all the way around", "always zero", "only at the start"],
correct: 1,
explain: "One path, one flow. It's the same everywhere in the loop.",
},
{
q: "Four bulbs in a row (series). One burns out. What happens?", kind: "concept",
options: ["The others get brighter", "Three stay on", "All four go dark", "Nothing changes"],
correct: 2,
explain: "Break the single loop and the whole thing goes dark — the old Christmas-lights problem!",
},
{
q: "Which arrangement keeps the OTHER bulbs glowing if one bulb dies?", kind: "concept",
options: ["Series (one road)", "Parallel (many roads)", "Neither", "Both the same"],
correct: 1,
explain: "Parallel branches are independent — one dying doesn't stop the others.",
},
{
q: "Putting pinches side by side (parallel) makes the TOTAL squeeze…", kind: "concept",
options: ["tighter", "looser", "disappear", "freeze"],
correct: 1,
explain: "More roads = easier for water. The total squeeze actually gets looser!",
},
{
q: "Your home's lights are wired in parallel so that…", kind: "concept",
options: ["they all turn off together", "one burning out doesn't kill the rest", "they use less wire", "they look prettier"],
correct: 1,
explain: "Parallel keeps each light independent — one dies, the others stay on.",
},
{
q: "Two branches side by side. How much push does each branch feel?",
kind: "concept",
options: ["They share it — half each", "Each feels the FULL push", "Only the first one gets push", "None"],
correct: 1,
explain: "Branches don't share the push! Each road gets the barrel's full pressure — what differs is how much flow each lets through.",
},
{
q: "Two pinches in a row. Which one uses up more of the push?",
kind: "concept",
options: ["The tighter pinch", "The looser pinch", "They always use the same", "Neither uses any"],
correct: 0,
explain: "The tighter squeeze is harder to get through, so it eats the bigger share of the push.",
},
{
q: "A volume knob on a speaker is secretly…",
kind: "concept",
options: ["a tiny drum", "a squeeze you can turn looser and tighter", "a battery", "a magnet"],
correct: 1,
explain: "It's a pinch with a knob! Turn it one way for more flow (louder), back for less (quieter).",
},
];
/* ─── App ───────────────────────────────────────────────────────────────── */
const TWEAK_DEFAULTS = /*EDITMODE-BEGIN*/{
"theme": "paper",
"showCircuit": true,
"audience": "adult"
}/*EDITMODE-END*/;
function App() {
const [t, setTweak] = useTweaks(TWEAK_DEFAULTS);
useCrossChapterPersistence(t, setTweak);
useEffect(() => { document.body.setAttribute("data-theme", t.theme); }, [t.theme]);
const kids = t.audience === "kids";
const navItems = [
{ id: "cover", label: "Cover" },
{ id: "big-idea", label: "Two shapes" },
{ id: "series", label: "Series" },
{ id: "parallel", label: "Parallel" },
{ id: "predict", label: "Predict" },
{ id: "rules", label: kids ? "Two rules" : "The rules" },
{ id: "playground", label: "Playground" },
...(kids ? [] : [{ id: "example", label: "Example" }]),
{ id: "practice", label: "Practice" },
{ id: "quiz", label: "Quiz" },
{ id: "whats-next", label: "What's next" },
];
return (
<>
setTweak("audience", v)} />
The Branching.}
chapterSub="Chapter 2 · Series & parallel"
kids={kids}
lede={kids
? <>Last chapter you had one pipe and one bulb. Now we'll hook up more. There are two ways to do it — and they behave very differently.
: <>Chapter 1 had a single resistor. Real circuits have hundreds. They're hooked together in exactly two flavors — series and parallel — and every clever thing in electronics is some recipe of the two.
} />
{
const a = rng.pick([2, 3, 4, 5, 6]), b = rng.pick([6, 8, 10, 12]);
return {
q: { adult: `Two resistors — ${a} Ω and ${b} Ω — are wired in series. What is their combined resistance?`,
kids: `Two pinches in a row: a ${a} and a ${b}. In a row you just add them. What's the total?` },
unit: "Ω", answer: a + b,
hint: "Series resistances simply add: R = R\u2081 + R\u2082.",
solution: { adult: `In series, resistances add: ${a} Ω + ${b} Ω = ${a + b} Ω.`, kids: `Add them: ${a} + ${b} = ${a + b}.` } };
},
(rng) => {
const a = rng.pick([2, 3, 4, 6]), b = rng.pick([3, 4, 6, 12]);
const r = +((a * b) / (a + b)).toFixed(3);
return {
q: { adult: `A ${a} Ω and a ${b} Ω resistor are wired in parallel. What is the combined resistance?`,
kids: `Now a ${a} and a ${b} sit side by side (parallel). What's the combined pinch?` },
unit: "Ω", answer: r, tol: 0.04,
hint: "Product over sum: (R\u2081·R\u2082) ÷ (R\u2081+R\u2082).",
solution: { adult: `Product over sum: (${a}·${b}) ÷ (${a}+${b}) = ${a * b} ÷ ${a + b} = ${r} Ω — less than either branch.`, kids: `Multiply, then divide by the sum: (${a}×${b}) ÷ (${a}+${b}) = ${a * b} ÷ ${a + b} = ${r}.` } };
},
(rng) => {
const a = rng.pick([2, 3, 4, 5]), b = rng.pick([4, 5, 6, 7]), v = rng.int(6, 24, 2);
const i = +(v / (a + b)).toFixed(3);
return {
q: { adult: `A ${v} V battery drives a ${a} Ω and a ${b} Ω resistor in series. What current flows?`,
kids: `${v} of push through a ${a} and a ${b} in a row. Flow = push ÷ total pinch. What's the flow?` },
unit: "A", answer: i, tol: 0.04,
hint: "Add the series resistors first, then I = V ÷ R.",
solution: { adult: `Series total = ${a + b} Ω, so I = V ÷ R = ${v} V ÷ ${a + b} Ω = ${i} A.`, kids: `Total pinch = ${a} + ${b} = ${a + b}. Flow = ${v} ÷ ${a + b} = ${i}.` } };
},
]} />
Series and parallel — every gadget you'll ever crack open uses both.
: <>Series and parallel are the bread and butter. Every analog circuit is some recipe of these two.
}
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