The river in the wire
Picture a mountain reservoir held high behind a dam, with a single pipe running down to the valley. The height of the water creates pressure — a push that wants to drive water down the pipe. Open a valve and water *flows*. Make the pipe narrower and the same pressure pushes less water through. That's it. That one picture contains almost everything you need to read your first electronic circuit, because electricity behaves astonishingly like water in a pipe.
In a circuit, the water pressure is voltage — the electrical 'push'. The water flowing through the pipe is current — the actual movement of charge. And the narrowness of the pipe is resistance — how strongly the circuit opposes that flow. Three quantities, three units: volts (V), amperes (A), and ohms (Ω). Memorize that trio; you'll use it for the rest of your life in electronics.
What voltage and current really are
Strip away the analogy and here's the physics. Wires are full of free electrons that normally jiggle about going nowhere. A battery is a chemical pump that piles up extra electrons at one terminal (the negative, −) and starves the other (the positive, +). That imbalance of charge is a stored *push* — a potential difference. One volt means one joule of energy is handed to each coulomb of charge that crosses it. A 9 V battery gives each coulomb nine joules of shove.
Connect a wire between the terminals and those electrons stream from the crowded side to the empty side. Current is simply the *rate* of that streaming: one ampere equals one coulomb of charge (about 6.24 × 10¹⁸ electrons) flowing past every second. So a small 19 mA current — the number we're about to calculate — is still roughly 120 quadrillion electrons sweeping past each second. The wire looks dead still; underneath, it's a torrent.
Ohm's law: the one equation to start with
In 1827 a German schoolteacher named Georg Ohm published the relationship that ties the trio together — so clean and so reliable that we named the unit of resistance after him. Ohm's law says the current through a resistor is the voltage across it divided by its resistance:
V V V
V = I × R I = ───── R = ─────
R I
V = voltage (volts, V) the push, measured ACROSS
I = current (amperes, A) the flow, measured THROUGH
R = resistance(ohms, Ω) the opposition
Mnemonic triangle — cover the one you want:
┌───────┐
│ V │ cover V → V = I × R
├───┬───┤ cover I → I = V / R
│ I │ R │ cover R → R = V / I
└───┴───┘The same law explains every everyday observation. Raise the voltage and more current flows (push harder, more water moves). Raise the resistance and current drops (a narrower pipe). And here's the part beginners under-appreciate: for an ordinary resistor, R is essentially *constant*. Double the voltage and you exactly double the current — a dead-straight line. That linearity is precisely what makes resistors so trustworthy as the building blocks of every circuit.
A worked example: a battery, a resistor, 19 mA
Time to use it for real. Take a fresh 9 V battery (the rectangular kind with two snap terminals) and a single 470 Ω resistor — one of the most common values in any beginner's parts drawer, marked with the colour bands *yellow-violet-brown*. Wire them in a loop. How much current flows? Don't guess — calculate.
Given: V = 9 V (the battery's push)
R = 470 Ω (the resistor's opposition)
Find I: I = V / R
= 9 V / 470 Ω
= 0.01915 A
≈ 19 mA (milliamps: 19 mA = 0.019 A)
Sanity check — does it round-trip?
V = I × R = 0.01915 × 470 = 9.00 V ✓
Note: 470 Ω across 9 V is a safe, gentle current.
A bare wire (R ≈ 0) across 9 V would try to pull
a huge current — that's a SHORT CIRCUIT. The
resistor is what keeps the current civilised.Power: where the energy actually goes
Current doesn't flow for free. As charge squeezes through the resistor, it gives up energy as heat — the same way water rushing through a narrow nozzle warms it. The rate at which energy is delivered is power, measured in watts (W), and it has its own beautifully simple law: power equals voltage times current.
Power law: P = V × I (watts = volts × amps) For our 470 Ω resistor on 9 V: P = V × I = 9 V × 0.019 A ≈ 0.17 W = 170 mW Two handy rewrites (substitute Ohm's law): P = I² × R = 0.019² × 470 ≈ 0.17 W ✓ P = V² / R = 9² / 470 ≈ 0.17 W ✓ Real resistors are sold with a power RATING — often 1/4 W (0.25 W). Our 0.17 W sits comfortably under that, so the resistor stays cool. Exceed the rating and it cooks, discolours, and eventually fails open.
This is why a phone charger gets warm, why a 100 W bulb is brighter than a 40 W one, and why engineers obsess over efficiency: every watt that doesn't do useful work leaves as heat that must go somewhere. Power is the bridge between the clean world of V, I, and R and the physical world of warmth, brightness, and battery life.
Reading the schematic — your first complete circuit
Engineers don't draw pictures of batteries and wires; they draw schematics — a shared shorthand where each part is a tidy symbol. Learn a handful and you can read circuits from any country and any decade. Here is our 9 V / 470 Ω loop, drawn the way it would appear in a textbook or a datasheet.
current I flows + → − (conventional)
┌───────────►────────────┐
│ │
──┴── + ┌─┴─┐
───── ┐ │ │ R = 470 Ω
──┬── │ 9 V battery │ │ (resistor)
───── ┘ └─┬─┘
│ − │
└───────────◄────────────┘
Battery symbol: long thin line = + terminal
short thick line = − terminal
Resistor symbol: a rectangle (IEC) — or a zig-zag
⌇⌇⌇⌇ in older US drawings.
A complete (CLOSED) loop = current can flow.
Break the loop anywhere (open switch, cut wire)
and current stops EVERYWHERE — instantly.- Find the source — here the battery. Note which terminal is + (long line) and which is − (short line).
- Trace the loop with your finger, leaving the + terminal and following the wire all the way around.
- Name each component you pass. Here, just one: the 470 Ω resistor that sets the current.
- Confirm the loop closes back at the − terminal. A closed loop carries current; an open one carries none.
- Apply Ohm's law: I = V / R = 9 / 470 ≈ 19 mA. You've now fully read and solved a real circuit.