When two or more resistors are connected in series, the current that flows through them is the same. Look at the picture.
The equivalent resistor is obtained adding all the resistors values, and we can find the current using the Ohm’s Law: I = V / Rs
Where Rs = R1 + R2 + R3
See the chart below where we find the original and the equivalent circuit.
To find out what the voltage on any of the resistor of the circuit is, we use a voltage divider formula.
We know that on a series resistor circuit the current is the same for all the resistors, so using the Ohm’s Law for each resistor we find the following formulas:
- I = Vin / Rs
- I = V1 / R1
- I = V2 / R2
- I = V3 / R3
These currents are the same so, Vin / Rs = V1 / R1.
Assuming that the voltage we want to know is V1, we clear this value. V1 = Vin x R1 / Rs. We can find V2 and V3 in the same way, using the corresponding resistor value.
In other words
Vout = (Resistance across the output / total resistance circuit) x Vin
With R1 = 1K, R2 = 2K and R3 = 3K
- Vout = Vin x R3 / ( R1 + R2 + R3)
- Vout = 12V x 3K / (1K + 2K + 3K)
- Vout = 12V x 3K / 6K = 12V / 2 = 6V
