Voltage division:

In a series circuit Ohm's law applies for each component.  However, since the current is common to all components we have:

          V1 = IR1,  V2 = IR2,  V3 = IR3

          Therefore  V1 ∝ R1,  V2 ∝ R2,  V3 ∝ R3

          i.e.    V_n ∝ R_n

Hence the voltage drops across each resistor can be calculated from the ratio of the resistance values.

It should also be noted, that for any given applied voltage we may derive any smaller voltages we wish by inserting resistors of the appropriate values in series. The following example shows how voltages of 8V, 4V and 24V can be derived from a 36V supply.

R_TOTAL = 12 + 6 + 36 = 54W

  54Ω = 36V and 1Ω = 36/54V

  12Ω = 36/54 ´ 12 = 8V across AB

and  6W = 36/54 * 6 = 4V across BC

and  36Ω = 36/54 ´ 36 = 24V across CD

A device which employs voltage division and which is commonly used in electrical and electronic circuits is the potential divider.  Here two or more resistors are used to divide a given input voltage to achieve a specified output voltage.  See diagram.

The potential divider is also known as a voltage divider or scaling circuit.

Note that if current is drawn from the output then the effective resistance of the circuit changes and the output voltage v_OUT changes.