Ohm’s Law in Practice
Design problems from start to finish: choosing parts that work, and stay cool.
The question
You want to light a yellow LED from a 9 V battery. Which resistor do you need, and how hot will it get?
What you’ll discover: how engineers use V = I × R and P = V × I together to choose safe parts, step by step.
In simple terms
BeginnerThe design recipe
Every time you add a part to a circuit, you can ask three questions:
- How much current should flow? (An LED: about 10 to 15 mA.)
- What resistance gives that current? R = V ÷ I.
- How much heat will the resistor make? P = V × I. Is that below its rating?
Answer all three, and your circuit works and stays cool.
Worked example: yellow LED on 9 V
- Target current: 12 mA = 0.012 A.
- Voltage for the resistor: 9.0 V − 2.1 V (yellow LED) = 6.9 V.
- Resistance: R = 6.9 ÷ 0.012 = 575 Ω. Round up to the next common (E12) value: 680 Ω. Check: 6.9 ÷ 680 ≈ 10.1 mA. Good.
- Heat: P = 6.9 V × 0.0101 A ≈ 0.07 W. A ¼ W (0.25 W) resistor handles that easily.
Go deeper
IntermediateMore design problems
Two LEDs, one battery: two red LEDs in parallel on 4.5 V, each at 10 mA. Each resistor: (4.5 − 2.0) ÷ 0.010 = 250 Ω → 270 Ω. Total current ≈ 2 × 9.3 mA ≈ 18.5 mA.
How long will the batteries last? Alkaline AA cells store very roughly 2,000 to 3,000 milliamp-hours (mAh) at small currents, though the real figure depends on the load and the temperature. At 18.5 mA, that’s very roughly 100 hours or more. (Three AAs in series still give the same mAh as one AA: series adds volts, not hours.) Battery capacity drops in the cold, which matters for anything left outside in a Lethbridge winter.
A voltage divider: to get about 1.5 V from 4.5 V, use R1 = 2 kΩ (2 × 1 kΩ in series) on top and R2 = 1 kΩ on the bottom: 4.5 × 1 ÷ 3 = 1.5 V. A divider only holds its voltage if whatever you connect draws very little current.
AdvancedTolerance and worst-case design
Real parts vary. A 5% 680 Ω resistor might be anywhere from 646 to 714 Ω; a fresh 9 V battery can read 9.5 V; LED forward voltages vary by a few tenths of a volt. Engineers check the worst case: highest supply voltage, lowest resistance, lowest forward voltage. Here: (9.5 − 1.9) ÷ 646 ≈ 11.8 mA, still safe.
Power ratings also fall at high temperatures (called derating), which is one reason designers keep resistors well below their rated power.
Quick check
What three questions should you ask when adding a resistor?
How much current should flow, what resistance gives that current, and how much heat will the resistor make.
What resistor would you use for a red LED on 4.5 V at about 15 mA?
(4.5 − 2.0) ÷ 0.015 ≈ 167 Ω → 180 Ω (or 220 Ω for a little less current).
How much power does a resistor use with 2.5 V across it and 11 mA through it?
P = 2.5 × 0.011 ≈ 0.028 W.
Words to know
- Standard value
- One of the resistor values actually manufactured, like 220 Ω or 680 Ω.
- Milliamp-hour (mAh)
- A measure of how much charge a battery can deliver.
- Worst case
- The combination of part variations that stresses a circuit most.
- Derating
- Using a part below its rating, especially when hot.
Learn more
Electronics School is part of the Discovery Zone. Every activity here runs on small batteries or a USB cable: never wall outlets. The one plug-in tool is the optional soldering iron, set up by an adult.