Question

The output of a certain voltage divider is 12 V with no load. When a load is connected, does the output voltage decrease?

Answer 1

Yes

Explanation:

The voltage at the output of the voltage divider is determined by the voltage dropped across the resistors in the divider.

[image source: https://www.allaboutcircuits.com/tools/voltage-divider-calculator/ ]

With no load, the current flowing in `R_1` is

`I_(R_1) = V_("in")/(R_1+R_2) " "(= I_(R_2))`

If a load (`R_L`) is connected to the output, (across `R_2`) the resistance at the output decreases from `R_2`, to `R_2` in parallel with `R_L`.

So `I_(R_(1_L)) = V_("in")/(R_1+(R_2|\|R_L)`

`(R_2|\|R_L) < R_2 ", so " I_(R_(1_L)) > I_(R_1)`

So we see that the current through `R_1` increases when a load is connected.

The voltage dropped across `R_1` therefore increases, so the voltage at the output decreases.