Ohm's Law and Power
Unit 3: Electricity and Electronics. Lesson 11 of 53 in BMET Academy.
One equation ties the three quantities together, and a second one tells you how much heat the circuit makes. Between them they answer most of the numeric questions on the exam and explain why electricity is dangerous.
Ohm's law
V = I x R volts = amps x ohms I = V / R amps = volts / ohms R = V / I ohms = volts / amps
The triangle trick: write V on top with I and R side by side underneath. Cover the one you want and the other two show you the operation. V over something means divide; two values side by side means multiply.
Worked example: 12 V across 4 ohm. Cover I, and you are left with V over R: 12 / 4 = 3 A.
Power
Power is the rate at which electrical energy turns into heat, light, or motion. It is measured in watts.
P = V x I the one to reach for first P = I squared x R when you know current and resistance P = V squared / R when you know voltage and resistance
Same example: 12 V at 3 A is 12 x 3 = 36 W.
Power ratings matter because every resistor is also a small heater. A common hobby resistor is rated a quarter watt. Ask it for more and it discolors, drifts, and eventually opens. In your lab, 9 V across 470 ohm draws about 19 mA and dissipates about 0.17 W, comfortably under the rating. Drop the resistor to 47 ohm and the same battery asks for 1.7 W, seven times the rating, and the part cooks.
Why Ohm's law is the safety lesson
Current is what injures people, and Ohm's law says what sets the current: the voltage available and the resistance in the path. The voltage of an outlet is fixed at 120 V. The variable is you.
Dry, intact skin about 100,000 ohm 120 V / 100,000 = about 1 mA a tingle Wet or broken skin about 1,000 ohm 120 V / 1,000 = 120 mA likely fatal
Nothing about the outlet changed. Sweat, a spilled bag of saline, a cut on your thumb, or a gel-covered electrode changed the denominator, and the current went up a hundredfold. That is the entire argument for dry hands, intact gloves, and keeping liquids off the bench.
A circuit worked end to end
A 9 V battery and one 470 ohm resistor in a loop:
- Current: I = V / R = 9 / 470 = 0.019 A, which is 19 mA.
- Power in the resistor: P = V x I = 9 x 0.019 = 0.17 W.
- Check it the other way: P = V squared / R = 81 / 470 = 0.17 W. The two agree, so the arithmetic is sound.
In the lab you measure the voltage and the current on that exact circuit, then compute R and P from your own readings instead of trusting the color bands. When a measured R lands within a few percent of the printed value, you have proved both the law and your technique.
This lesson includes an interactive lab in the course.
Ohm's Law and Power, explained slowly
The triangle, and why it works
V
-------
I | R
cover V -> V = I x R
cover I -> I = V / R
cover R -> R = V / IThe three forms are one relationship read three ways: the current through a resistance is proportional to the voltage across it. Double the push and you double the flow. Double the opposition and you halve the flow.
Worked examples to copy
Known Find Work Answer 12 V across 4 ohm current 12 / 4 3 A 0.5 A through 100 ohm voltage 0.5 x 100 50 V 9 V and 19 mA measured resistance 9 / 0.019 about 474 ohm 120 V across 1,000 ohm current 120 / 1000 0.12 A = 120 mA 24 V, need 10 mA resistance 24 / 0.010 2,400 ohm
The third row is the lab. You measure the voltage and the current and compute a resistance you never measured, then compare it with the color bands. When they agree you have proved your technique as well as the law.
Power: the other equation
P = V x I volts x amps P = I squared x R when current and resistance are known P = V squared / R when voltage and resistance are known 12 V at 3 A = 36 W 0.019 A in 470 ohm = 0.019 x 0.019 x 470 = 0.17 W 9 V across 470 ohm = 81 / 470 = 0.17 W
The last two rows are the same circuit computed two ways, which is a free check on your arithmetic: if two routes disagree, one of them used a wrong number.
Power matters because it is heat. A resistor is rated for the heat it can shed, commonly a quarter watt on a hobby part and one or more watts on power resistors. Asking a quarter-watt part for 1.7 W does not blow it instantly; it discolors, its value drifts, the device develops an intermittent fault, and weeks later it opens. Burnt or discolored resistors on a board are a message: either the part was underrated or something else failed and overloaded it. Replacing it without finding out which is how you get the same board back.
The shock arithmetic
Ohm's law is the reason electrical safety numbers are what they are. The outlet's 120 V is fixed; the path resistance is not.
Path Resistance Current from 120 V Effect dry hand to dry hand about 100,000 ohm about 1.2 mA perception, a tingle sweaty hands, metal tools about 10,000 ohm 12 mA past let-go: cannot release wet skin, standing in water about 1,000 ohm 120 mA fibrillation likely
Nothing about the electricity changed in those three rows. Your skin did. That is the argument for dry hands, intact insulation on your tools, no rings or watches at the bench, keeping fluid away from powered equipment, and never making yourself the second connection to ground.
The same arithmetic in reverse explains microshock: a current as small as 10 microamps delivered directly to the heart through a catheter or a pacing lead can cause fibrillation, because the skin's resistance is not in the path at all. Microamps outside the body are nothing; microamps inside it are the reason leakage limits exist.