How do we predict if power loss will increase or decrease in a DC circuit?
If you look at this problem qualitatively, if the variable load resistance is either infinite or zero there is no power dissipation in the variable resistor load. So if we had an expression for the power dissipation in the variable load as a function of variable load resistance it would have a maxima at the series R0 resistance (we could guess, since that's like source resistance) and would decrease on either side.







simulate this circuit &ndash; Schematic created using CircuitLab

We can derive this expression- current is V/(R0 +R), and power dissipation in the variable load R is \$I^2 R\$,  so load dissipation is \$V^2 R\over {(R0 + R)^2 }\$

Plot some typical values to get an idea: (V =5V, R0 = 5\$\Omega\$)



If you differentiate that expression wrt R to find the maxima you get
 \$-V^2 (R - R0)\over {(R + R0)^3}\$ , which is 0 at R = R0, as expected.

The curve is not monotonic- it decreases on either side of the series resistor value.