Ohm's law

Three letters, one rule

The last episode gave each part of a circuit a name: voltage (V) is the push, current (I) is the flow, and resistance (R) is the squeeze. Ohm's law links them in one line:

V = I × R

Voltage is in volts (V), current in amps (A) and resistance in ohms (Ω). The units fit together because one ohm is defined as one volt per amp. The rule is named after Georg Ohm, who published it in 1827.

Find any one from the other two

Rearrange the same rule to get whichever value is missing:

• Voltage: V = I × R
• Current: I = V ÷ R
• Resistance: R = V ÷ I

A memory trick is the Ohm's law triangle: V on top, I and R side by side below. Cover the one you want, and the other two show you the sum. Cover I and you see V over R, so divide.

A worked example

Put a 12 V battery across a 4 Ω resistor. The current is 12 ÷ 4 = 3 A.

• Double the resistance to 8 Ω, keep 12 V: 12 ÷ 8 = 1.5 A. The current halves.
• Double the voltage to 24 V, keep 4 Ω: 24 ÷ 4 = 6 A. The current doubles.

Current goes up with the push and down with the squeeze. Engineers use this to choose parts before building anything, so nothing carries more current, or gets hotter, than it can handle.

Try it yourself

Pick any two numbers and find the third. What current flows when a 9 V battery drives a 3 Ω resistor? (9 ÷ 3 = 3 A.) What resistance lets 0.5 A flow from a 6 V supply? (6 ÷ 0.5 = 12 Ω.)

Good to know

• Ohm's law holds for "ohmic" materials such as resistors and metal wires at a steady temperature. It isn't a law of nature: diodes, LEDs and hot lamp filaments don't follow it simply.
• The example ignores the battery's own internal resistance and the wires' resistance, so a real 12 V battery into 4 Ω would give a little less than 3 A.
• 3 A through 4 Ω turns 36 watts into heat, so a real resistor would need a high power rating. Power gets its own episode later.
• The letter I comes from the French intensité (current intensity). Some books write the rule as E = IR.