Voltage Dividers.

        Voltage dividers are found in many places including volume controls and especially in circuits with resistive sensors.  (By putting a resistive sensor in a voltage divider, you can produce a changing voltage when the resistance of the sensor changes in response to a change in a physical variable!)

        Here is the circuit for the basic voltage divider.

        In this circuit, you need to note the following:

• There is a voltage source, V_in.  The voltage source produces a voltage across the combination of R_a and R_b.
• Current flows through the two resistors.  If there is no load attached to the output (where you see V_out), then the same current flows through both resistors.  If there is a load attached that draws current, then the analysis is not going to hold.
• This link will take you to the analysis of this circuit.  The result is:
• V_out = V_in R_b/( R_a + R_b)

        If one of the resistors (either one) changes (due to some physical variable changing) then the output voltage will change.  That makes this circuit useful for measurement applications.  Resistive sensors (that have a resistance that changes with some physical quantity) include the following:

• Thermistors - which change resistance when temperature changes.
• Photoresistors - which change resistance when light intensity changes.
• Strain gages - which change resistance when there is a strain change in the device they are attached to.  (Used to measure strain in bridges, buildings, aircraft wings under load, etc.)