*"Theorem: the power dissipated by the transistor is not larger than 1/4 of the power that would be dissipated by the two resistors R3 and R4 if they were directly connected."*[R3 and R4 are Load and Emitter resistors in that circuit.]

I simplified this to just think about resistors in series. If one adds a new resistor in series with others, its power dissipation can never exceed a quarter of what the rest of the resistor chain dissipates without that resistor. Here is a screenshot of my LTSpice simulation:

It abuses a voltage source to create a time-varying resistance (idea pinched from http://www.instructables.com/id/LTSPICE-Voltage-Controlled-Switch-and-Resistor/) where I use a sine wave to vary the resistance from 0.01 ohm (LTSpice won't deal with 0 resistance) to 2000 ohms. In the five panes we see the voltage (but interpret it as resistance), the power dissipation of R1 (400 watts peak when R2 is zero) the voltage across R2 as its resistance varies, the current in the circuit, and the power dissipation of R2 over time.

Sure enough, the R2 power dissipation peaks at 1/4 of the power peak of R1. It twin-peaks when R2 = R1 = 100 ohms.

Is this a reliable and generalizable rule-of-thumb? If you need to add a component, its power dissipation won't exceed 1/4 of the dissipation in the loop if that component were short-circuited?

If I have confused any of this, please set me straight or give me a counter-example.

Thanks

Peter