Explain the LED current-limiting resistor with Ohm's Law

In a circuit, three numbers always move together: voltage (V), current (I), resistance (R). When you change one, at least one of the others adjusts — this is not a simple arithmetic rule but a physical law of balance. In repair language: if you focus on only one variable on a board, you miss what the other two are quietly doing.

Physically the relationship is this: voltage represents the imbalance between two points, resistance the obstacle this imbalance presents to flow, and current the resulting motion of charge. The formula V = I × R compresses these three into a single line.

The equation opens three interpretations:

• Hold V constant: as R increases, I decreases; as R decreases, I increases. This is the essence of typical LED protection.
• Hold R constant: as V increases, I increases proportionally. The thing to watch when changing an adapter.
• Hold I constant: V and R increase proportionally. Encountered in sensor-supply design.

All three readings are true at the same time — your workshop thinking must carry all three together.

Visual reading: The Ohm's Law triangle — voltage (top, emerald), current (lower left, cyan), resistance (lower right, amber); along the sides, V=I×R, I=V/R, R=V/I; the three tied to one equation.

Knowing a formula by rote is not enough; in the workshop, a formula is used not just for calculation but for decisions. 'This line is putting out 1.8 V, expected 3.3 V — there is a resistance drop here; what value of resistor produces that difference?' To answer this, you must be able to invert the formula.

Intuitive grasp comes through three moves:

1. Single-variable move: Read R = V / I as 'I measured V, I am estimating I, what remains is R that I derive.'
2. Sense of direction: As R grows, I shrinks — see this in your mind's eye without looking at the numbers. When the resistance value doubles, halving the current should feel natural.
3. Unit cadence: 1 V × 1 A is not 1 Ω; 1 V / 1 A = 1 Ω. That is the definition of the ohm — but in repair, the working units are usually mA and kΩ. You need to know practical ranges like 5 / 470 ≈ 10 mA (that is, 5 V / 470 Ω ≈ 10 mA).

Do not think of the formula only as an equation; place the triangle of three numbers inside your head. V at the top, I and R at the two lower corners — cover one and the math of the other two emerges.

The LED calculation is the most concrete Ohm's-Law application in repair. Because the LED is 'a component with its own voltage drop' (red typically 2 V, blue/white typically 3 V) — if you do not limit the current with a resistor, it does not limit itself, and it can be damaged directly.

The 4 steps of the calculation:

1. Write down the source voltage: V_source = 5 V (typical USB)
2. Subtract the LED drop: V_LED = 2 V (red LED) → V_resistor = V_source − V_LED (i.e., 5 V − 2 V → 3 V remains)
3. Pick a target current: I_target = 10 mA (safe educational range for an LED: 5-20 mA)
4. Compute the resistor: R = V_resistor / I_target → R = 3 / 0.010 = 300 Ω → nearest standard value 330 Ω

The output formula: R = (V_source − V_LED) / I.

Practical check — numerical speed:

• 5 V source, 2 V LED, 470 Ω → I = 3 / 470 ≈ 6.4 mA → safe, slightly dim
• 5 V source, 2 V LED, 220 Ω → I = 3 / 220 ≈ 14 mA → safe, bright
• 5 V source, 2 V LED, 100 Ω → I = 3 / 100 ≈ 30 mA → risky; unnecessarily high for most small LEDs
• 5 V source, 2 V LED, 0 Ω (no resistor) → in practice the source and LED limit the current; the LED can be damaged in a short time

Being able to estimate these numbers in your head lets you answer 'how am I going to drive this LED' in 5 seconds at the bench.

The current through a resistor changes directly proportionally to the voltage across it. That is, if you double the voltage, the current doubles too as long as the resistance value stays the same — this is a linear behavior, unlike components with a voltage drop such as LEDs. In repair, resistors are predictable reference points; LEDs or transistors are not as linear.

Quick table (R = 470 Ω constant):

• V = 1 V → I = 1/470 ≈ 2.1 mA
• V = 3 V → I = 3/470 ≈ 6.4 mA
• V = 5 V → I = 5/470 ≈ 10.6 mA
• V = 12 V → I = 12/470 ≈ 25.5 mA
• V = 24 V → I = 24/470 ≈ 51 mA → heat risk becomes pronounced for small resistors

The resistor's power limit (important): A resistor is chosen not only by its resistance value but also by its power rating. The formula P = V × I = V² / R means about 0.3 W of power dissipation for 470 Ω at 12 V; a standard 1/4 W (0.25 W) resistor exceeds this threshold and heats up. At 24 V, the same resistor is about 1.2 W; for a 1/4 W resistor, this is now the damage zone. We will learn the details tomorrow.

Practical workshop reflex: When reading the current on a line, check whether that current is coming through the resistor; if the change is not proportional, the resistor may have opened, its value may have drifted, or it may be approaching a short.

Calculation stays abstract; pick up a battery, an LED, and three resistors, and verify the calculation-vs-measurement match yourself. This is preparation for the day you will take real measurements with a multimeter in G5.

Setup:

1. 5 V source (USB power bank, or a 9 V battery + 7805 / AMS1117-5V regulator — the source must actually be 5 V; the table below is calculated assuming 5 V)
2. Same LED (red, ~2 V drop assumed)
3. Three resistors: 220 Ω, 470 Ω, 1 kΩ

Calculation (with paper first, then experiment):

• 220 Ω → I = 3 / 220 ≈ 13.6 mA → bright but safe
• 470 Ω → I = 3 / 470 ≈ 6.4 mA → medium brightness
• 1 kΩ → I = 3 / 1000 ≈ 3.0 mA → visible but faint

Expected observation:

• As the resistor grows, the LED should glow more dimly
• Dimness is not linear — your eye perceives it logarithmically; the difference between 220 Ω and 1 kΩ does not look 'twice as bright', only 'noticeably brighter'
• All 3 LEDs should light; none should burn out

If you get an unexpected result: The LED is installed backwards (won't light), the resistor value is wrong (color-code reading error), or the battery has dropped (source voltage is less than 5 V). Check these three possibilities in order.