Here's another voltge divider circuit.  In this case there is a light sensitive resistor, R_L. The light senstive resistor has two values.

• In the dark it has a resistance, R_dark =  500,000W (500kW).
• In the light it has a resistance, R_light =  1000W (1kW).

It is exposed to both light and dark at different times, and it is desired to have a circuit that will give a large signal - close to 5 v - when the sensor is exposed to a dark situation, and a small signal - close to 0 v - when the sensor is in the light.

 

The problem here is to produce the best possible logic signal at the output voltage terminals in the sense that the total error.  (Click here for a more extensive explanation of the situation.)

• Your problem is to derive an analytical expression to calculate the value of R_a that produces the lowest total error (Sum of the error in the light and the error in the dark).