Video narration
How can a messy resistor network become one battery and one resistor? Take a 12-volt circuit with 2-kilohm and 4-kilohm divider resistors, and use its two output terminals for the load. Thevenin’s theorem says this linear network, viewed from those terminals, becomes a voltage source, Vth, in series with Rth. Remove the load: the terminal voltage is the open-circuit voltage, so Vth equals 12 times four-sixths, or 8 volts. Turn off independent sources: short an ideal voltage source, open an ideal current source. Here, Rth is 2 kilohms in parallel with 4 kilohms, giving 1.33 kilohms. Now the network stops being components and becomes a two-number model: Vth and Rth. With a 1-kilohm load, Iload equals Vth divided by the sum of Rth and Rload: 8 divided by 1.33 plus 1, or about 3.43 milliamps. That answers it: find open-circuit voltage and resistance with sources turned off; the messy network becomes one battery and one resistor.