How Power and Current are Affected by Resistance

In keeping with the simple voltage divider theme, let's look at a similar circuit:

Here, R1 can be varied from 0Ω to 25Ω.

What is the voltage across R1?

Use the voltage divider formula - V (across R1) = (24volts x R1)/(R1+R2+R3)

So if R1 is 0, then the volts across it are zero.

If R1 is at its maximum of 25Ω then the volts across it will be 20 volts.

Now for a new thing:

Power

Power can be computed several ways, but the easiest is just that power is current x voltage of a component.

So the power dissapated (consumed and radiated away as heat) for R1 is
(Voltage across R1) x (Current through R1)

So if R1 = 0, the power is zero.

If R1 = 25Ω what is the power?

Well we know the volts, but we need the current:  I = 24V / (4+1+25) = 0.8 amps

So the power is now just 20 volts x 0.8 amps.  Which is 16 Watts.

But the maximum power does not occur when R1 is minimum or maximum: (0 or 25Ω).

See the graph below:

Power seems to peak when R1 = 5Ω.

Why?