Energy forms on graphs and on fractals can be interpreted in terms of electric linear networks by assuming that current flows between nodes (vertices) connected by resistors (edges). A resistor is called a dissipative element because there is a loss of energy when an alternating current runs through it. To the contrary, no loss is caused when the current flows through a non- dissipative element such a conductor or a capacitor.

However, in the 60s Feyman described an infinite passive linear network (the infinite ladder), whose nodes were connected by conductors and capacitors, that would lead to actual power dissipation. Based on this idea, we introduce in this talk the concept of power dissipation on graphs and fractals associated to passive linear networks with non-dissipative components. We present and discuss in detail the so-called Sierpinski ladder fractal net- work: we construct the power dissipation measure associated with continuous potentials in this network and prove it to be continuous as well as singular with respect to an appropriate measure defined on the fractal dust related to the network.