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Concepts

The theory behind every circuit — the rules the simulator obeys.

The circuit loop

Current only flows around a CLOSED loop: out of the battery’s + terminal, through every part, back into −. Break the loop anywhere and everything stops. That’s all a circuit is — a round trip for charge.

no loop → I = 0

Ohm’s law

Voltage pushes, resistance resists, current is what results. Double the resistance and half the current flows; double the voltage and it doubles. Every readout in this game obeys this one line.

V = I × R (so I = V/R and R = V/I)
9V across 200Ω → I = 9/200 = 45mA

Electrical power

Power is how fast energy is delivered — what makes lamps bright and parts hot. It’s voltage times current, so a lamp glows brightest when it gets both volts across it and amps through it.

P = V × I = I²R = V²/R
4.5V × 100mA = 0.45W

Series vs parallel

In series, parts share one path — the same current flows through each, and resistances ADD. In parallel, parts offer separate paths — each gets the full voltage, and total resistance DROPS. Most circuit design is choosing between these two.

series: R = R₁+R₂ · parallel: 1/R = 1/R₁+1/R₂

Current limiting

Some parts (LEDs especially) don’t limit their own current — connect them straight to a battery and they fry. A series resistor sets the current: the resistor takes the leftover voltage, and Ohm’s law tells you what flows.

R = (V_supply − V_f) / I_target
(9V − 2V) / 15mA ≈ 470Ω

Diodes: one-way streets

A diode conducts in only one direction, and only after its forward voltage (~0.7V, LEDs ~2V) is overcome. Backwards, it blocks entirely. That asymmetry is the seed of ALL electronics.

forward: V_f ≈ const · reverse: I ≈ 0

The voltage divider

Two resistors in series split the supply voltage in proportion to their resistances. The midpoint voltage is the workhorse of sensing: swap one resistor for a sensor and the midpoint moves with light or temperature.

V_out = V × R₂/(R₁+R₂)
9V with 1k over 2k → 9 × 2/3 = 6V

Fuses: sacrificial protection

A fuse is a thin wire that melts when too much current flows, breaking the circuit before anything expensive burns. It protects by dying — always size it above normal current but below what your parts can survive.

I > rating → blown

Using meters

An ammeter measures current THROUGH itself, so it goes IN the loop (series) and has near-zero resistance. A voltmeter measures voltage ACROSS two points, so it connects in parallel and has huge resistance. Swap them and you get a short or a broken loop.

ammeter: series, R≈0 · voltmeter: parallel, R≈∞

The Wheatstone bridge

Two voltage dividers side by side; a meter spans their midpoints. When the ratios match, the bridge is balanced and the meter reads zero — tiny imbalances become measurable. This is how precision sensing works.

balanced: R₁/R₂ = R₃/R₄

Capacitors & RC time

A capacitor stores charge; current flows only while its voltage is catching up to the supply. With a resistor in the path, the catch-up takes time — the RC time constant. That’s how circuits remember, delay, and smooth.

Q = C×V · τ = R×C
1kΩ × 1000µF → τ = 1s

Relays: current controls current

A relay is a switch thrown by an electromagnet: enough current through the coil pulls the contact over. A small, safe current can switch a big one — the mechanical ancestor of the transistor.

I_coil ≥ pull-in → contact closes

Systematic fault-finding

A dead circuit fails for exactly one reason at a time: an open (break) or a short (unwanted path). Probe voltages: a full supply voltage across ONE part means it’s open; zero volts across a part that should drop some means it’s shorted or bypassed.

open part: drops full V · shorted part: drops 0V

Transistors: the electronic switch

A tiny base/gate current or voltage controls a much larger collector current — a relay with no moving parts, millions of times faster. Amplifiers, logic, computers: all built from this.

small input → large controlled output

Ratings & burnout

Every real component has a limit — a lamp’s wattage, an LED’s max current, a resistor’s power rating. Push past it for long and the part overheats and burns out (goes open, dead). The fix is always the same: limit the current or spread the load so each part stays safely under its rating.

stay under: P = V·I < rating · derate for headroom
LED max 25mA → series R = (V−V_f)/0.02 keeps it safe

Inductors & electromagnets

Current through a coil builds a magnetic field, and the coil fights any CHANGE in that current. Steady current passes freely; sudden changes are resisted. The stored field is also what pulls relay contacts.

V = L × dI/dt

Components

Everything on the shelf, with the physics each part obeys.

Power

9V
Battery

The classic power source: a fixed voltage between + and −. It pushes current around the loop and every circuit needs a push.

Fixed EMF; delivers P = V × I to the loop.
12.0V− PSU +
Power Supply

An adjustable bench source — like a battery whose voltage you can dial.

Fixed EMF at the set voltage.
5.0V · 1.0Hz
Function Gen

A source that wiggles: sine or square waves at a chosen frequency and amplitude. The tool for exploring how circuits respond to CHANGE.

V(t) = A·sin(2πft) — watch it on the scope.
20mA
Current Source

The battery’s dual: instead of fixing the voltage, it forces a fixed CURRENT through whatever it feeds.

I fixed; V adjusts to whatever the load demands.
Ground

The reference point — 0V by definition. Voltages are always measured relative to somewhere; ground is the agreed somewhere.

V ≡ 0 at this node.

Passives

1kΩ
Resistor

The workhorse. It resists current flow, drops voltage, limits, divides, and turns electrical energy into heat.

Ohm’s law: V = I × R.
10kΩ · 50%
Potentiometer

A resistor with a movable tap (wiper). Twist it to change the split — volume knobs and dimmers are potentiometers.

The wiper divides R into two parts; V_out follows the ratio.
🎮 Select it and drag the Wiper slider in the panel on the right.

Storage

1mF
Capacitor

Stores charge like a tiny rechargeable tank. Passes changing current, blocks steady DC — the memory and timing element of circuits.

Q = C×V; with a resistor, τ = R×C sets the timing.
20H
Inductor

A coil that stores energy in its magnetic field and fights any change in current. Electromagnets, filters, and relay coils are inductors.

V = L × dI/dt — steady current flows freely.

Semiconductors

diode
Diode

A one-way valve for current: conducts forward after ~0.7V, blocks completely in reverse.

Forward: V_f ≈ 0.7V. Reverse: I ≈ 0.
5.1V zener
Zener Diode

A diode designed to break down at a precise reverse voltage — and survive it. The classic cheap voltage reference.

Reverse: clamps at V_z regardless of current.
NPN
NPN Transistor

The electronic switch and amplifier: a small base current lets a much larger collector current flow.

I_c ≈ β × I_b — current controls current.
PNP
PNP Transistor

The NPN’s mirror twin: it turns ON when its base is pulled LOW. Useful for switching the + side of a load.

Conducts when V_base < V_emitter − 0.7V.
NMOS
MOSFET (N)

A voltage-controlled switch: no gate current at all, just a threshold voltage that opens the channel.

Conducts when V_gate exceeds V_threshold.

Switches & Relays

off
Switch

The simplest control: open (no path) or closed (a plain wire). Everything digital descends from this idea.

Open: I = 0, full V across the gap. Closed: R ≈ 0.
🎮 Click the switch on the canvas to flip it open or closed.
up
Two-Way Switch

Single pole, double throw: one input that connects to either of two outputs — an electrical fork in the road.

Always exactly one path closed.
🎮 Click it on the canvas to throw the lever between its two outputs.
push
Push Button

A momentary switch — closed only while held. Doorbells, keyboards, and reset buttons.

Spring-loaded: releases back to open.
🎮 Click and HOLD the button on the canvas — it springs back when you let go.
coilNONC
Relay

A switch thrown by an electromagnet: enough coil current pulls the contact over. Small currents switching big ones — the mechanical ancestor of the transistor.

Coil ≥ ~12mA pull-in → contact closes.
🎮 No clicking needed — enough coil current pulls the contact over by itself.

Output

lamp
Lamp

A filament that glows when current heats it. Brightness follows power — the game’s favorite way to SHOW you the circuit state.

P = V²/R; full brightness ≈ 0.9W.
LED
LED

A diode that turns current into light. Greedy above its forward voltage — always give it a series resistor.

V_f ≈ 2V; set brightness via I = (V_supply − V_f)/R.
buzzer
Buzzer

Turns current into sound. Polarity matters; volume follows power.

P = V × I drives loudness.
Mmotor
DC Motor

Turns current into rotation. Reverse the current and it spins the other way — the heart of every polarity puzzle.

Speed follows power; direction follows current sign.

Sensors

80% · 398Ω
Photoresistor

A light-dependent resistor: bright light → low resistance, darkness → high. Put it in a divider and light becomes a voltage.

~100Ω in full light → ~100kΩ in the dark.
🎮 Select it and set the Light level slider in the panel on the right.
🌡 25°C · 10kΩ
Thermistor (NTC)

A temperature-dependent resistor. The sensing element in thermostats — heat changes resistance, resistance changes voltage.

R falls as temperature rises (NTC).
🎮 Select it and set the Temperature slider in the panel on the right.

Meters

A0Aseries
Ammeter

Measures current THROUGH itself — wire it into the loop (series). Nearly zero resistance so it doesn’t disturb what it measures.

Series placement; R ≈ 0.
🎮 Wire it IN the loop (series) — it shows the current flowing through.
V0Vparallel
Voltmeter

Measures voltage ACROSS two points — connect it in parallel. Huge resistance so almost no current detours through it.

Parallel placement; R ≈ 10MΩ.
🎮 Wire its pins ACROSS a part (parallel) — it shows the voltage between them.

Protection

1A
Fuse

Sacrificial protection: a thin wire that melts above its rated current, breaking the circuit before anything expensive burns.

I > rating → blown (click to replace).
🎮 A blown fuse shows a broken filament — click it to fit a fresh one.

The best way to learn any of this: build it in the sandbox and watch the numbers.