Lessons · Electrical · the voltage divider
Where the volts go: in proportion to the ohms
In a series loop each part takes a share of the source voltage equal to its share of the total resistance: Vx = Vsource × Rx / Rtotal.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Two identical heaters wired in series by mistake each get half the volts and a quarter of the heat. A thermostat sensing circuit, a dimmer, and a loose connection eating volts before they reach the load are all this one rule.
How to think about it
Add the resistances for the total. The fraction each part gets is its resistance over the total. Multiply by the source. Check: the shares add up to the source voltage, every time.
Worked example
R = 100 Ω + 400 Ω = 500 ΩThe total the source sees.
V across the 400 Ω = 24 V × 400 / 500 = 19.2 VFour fifths of the resistance gets four fifths of the volts.
V across the 100 Ω = 24 V × 100 / 500 = 4.8 VThe rest. 19.2 + 4.8 = 24: nothing lost, nothing invented.
Your turn
A 12 V source across 2 Ω and 4 Ω in series. Write the line for the volts across the 4 Ω.
V = 12 × 4 / = 8 V
Solve one, graded on the server
The trap
Using the part's resistance over the other part instead of over the total. 400 / 100 is 4, and 24 × 4 is nonsense. The denominator is always the whole loop.