The Three Numbers · Build Electronics

⟨ fragment 02 · transmission begins ⟩

We measured the push, the flow, and the fight, and found one rule binding all three. Learn it, and no circuit will surprise you again.

⟨ transmission ends ⟩

By the end of this page you will predict a circuit’s current before you connect anything, and choose an LED’s resistor by calculation instead of luck. Three numbers do all of it, and one rule ties them together.

The three numbers have names. Volts (V) measure the push, amps (A) measure the flow, and ohms (Ω) measure how hard a part fights the flow. A milliamp (mA) is a thousandth of an amp; bench currents usually live there. Below is a plain loop: an adjustable supply and a 470 Ω resistor, with a meter on each number. Turn the supply and watch all three.

Instrument 01 · volts push, amps flow

Turn the supply knob and watch the meters.

SUPPLY 9.0 V

V I R

One 470 Ω resistor and an adjustable supply, no LED in this loop. The dots and the motor's propeller speed up with the current; at the 9 V start the loop carries 9 ÷ 470 ≈ 0.019 A, which is 19 mA. The motor here is a pure current indicator: in this model it adds no resistance, so the 470 Ω alone sets the flow. Real motors fight back; that story comes later on the road.

Ohm’s law

V = I × R

V — voltage, in volts (V): the push across the part

I — current, in amps (A): the flow through the part; 1 mA = 0.001 A

R — resistance, in ohms (Ω): how hard the part fights; 1 Ω lets 1 V push 1 A

It reads three ways, and you just felt the first: I = V ÷ R says what will flow. R = V ÷ I names a part from what you measure. V = I × R finds the push a flow needs. Same rule, turned to face whichever number you are missing.

9 V ÷ 470 Ω ≈ 19 mA, the loop above at its starting knob

4.5 V ÷ 470 Ω ≈ 9.6 mA: half the push, half the flow

The rule works before a circuit exists: current is a prediction, not a surprise. The bench below is 9 V behind 1 kΩ, and the switch is still open. Work out I = V ÷ R in your head, drag your mark onto the meter, then click the switch closed and see.

Instrument 02 · predict, then connect

Drag your mark onto the meter scale: how many mA will flow?

V R I

A 9 V battery behind 1 kΩ, which is 1000 Ω. The meter reads 0 to 15 mA. Until the switch closes, nothing flows and the needle rests at 0.

Now size the guardian from First Light by calculation instead of trust. An LED is not a resistor: it keeps a nearly fixed slice of the push for itself, and the series resistor gets the rest. The size of that slice is the LED’s own number, printed in its datasheet, and different colors keep different amounts. The red on this bench keeps 1.9 V. So the recipe below sizes the resistor for the current you want. This bench’s red is comfortable at 15 mA, the current its loop carried in First Light.

the LED resistor recipe

R = V − V_LEDI

R — the series resistor, in ohms (Ω): what you are choosing

V — the supply voltage, in volts (V): the whole push

V_LED — the LED’s forward voltage, in volts (V): the slice the LED keeps: its own datasheet’s number; 1.9 V for this bench’s red

I — the wanted current, in amps (A): what the LED should carry

9 V − 1.9 V = 7.1 V for the resistor, with this bench’s 1.9 V red

7.1 V ÷ 0.015 A ≈ 473 Ω; the nearest real part is 470 Ω

Instrument 03 · size the guardian

Drag a resistor from the bin into the empty seat.

I LIGHT

The 9 V loop from First Light; the LED keeps 1.9 V. Seated: 100 Ω gives 71 mA, far beyond what the LED survives; 1 kΩ gives 7.1 mA, lit but dim; 470 Ω lands the comfortable 15 mA.

One turn of the rule is left: naming a part you cannot read. The resistor below hides its value under a sleeve, but the bench shows 6 V of push and the meter reads 20 mA of flow. Two knowns decide the third: dial in what the hidden resistor must be.

Instrument 04 · name the hidden part

Slide your answer: R = V ÷ I.

YOUR R 50 Ω

V I

6 V across the sleeved part pushes 20 mA, which is 0.020 A. The dial checks your answer against the loop itself.

When you are ready, test yourself. Three questions from real benches:

Your supply is 5 V, and a red LED should carry 10 mA and keeps 2 V for itself. Which series resistor?

A 2.2 kΩ resistor sits across a fresh 9 V battery. How much flows?

A mystery resistor passes 3 mA with 6 V across it. Its value?

You now hold the rule most of this road leans on. One honest caveat: not every part obeys it. Your LED never did, it keeps its 1.9 V slice whatever flows, and First Light showed it passes one way only. Resistors obey it exactly, and the next fragment, The Resistor, teaches you to read their stripes and choose from the values that actually exist.

Lesson 2 done.

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