Norton's theorem says the identical thing as Thevenin's in the other dialect: the box is a current source in parallel with a resistance. The resistance is the same $R_{Th}$; the source is $I_N$, the Norton current, in amperes — and it is what the terminals deliver into a dead short, since a short leaves nothing but the internal resistance in the way. So $I_N = \dfrac{V_{Th}}{R_{Th}}$ — I-N equals V-Th over R-Th, with $V_{Th}$ the Thevenin voltage in volts and $R_{Th}$ the Thevenin resistance in ohms. Read it backwards, $R_{Th} = V_{Th}/I_N$, and two bench readings — open circuit and short circuit — give you the resistance without a test load at all.

Now the question the theorems were invented for. Connect a load $R_L$ and ask which value takes the most power. Too small and it draws plenty of current but almost no volts land on it; too large and it holds the volts but barely any current flows. The peak sits exactly in the middle, where $R_L = R_{Th}$ — the matched load — and there the power delivered is $P_{max} = \dfrac{V_{Th}^{2}}{4 R_{Th}}$, in watts. Read aloud: P-max equals V-Th squared over four R-Th.

Where does the 4 come from? At the match the loop resistance is $2R_{Th}$, so the load sees half the source voltage — and power goes as voltage SQUARED, so half the volts is a quarter of $V_{Th}^2/R_{Th}$. Two halvings, one factor of four. Forgetting that 4 is the classic slip in this whole chapter, and it overstates the answer fourfold, which on a resistor's wattage rating is the difference between a part and a smell.

One honest caveat, because it changes what the theorem is FOR. At the match the source burns exactly as much inside itself as it delivers — fifty percent efficiency, on a good day. Matching is what you do for signals, where the last microwatt of information matters. It is emphatically not what you do for power distribution, where the whole game is keeping the source resistance as far below the load as you can.