TITLE: Applications of Kirchhoff's circuit laws to graph theory
QUESTION [15 upvotes]: Is there a good survey on applications of Kirchhoff's circuit laws to graph theory or/and discrete geometry? 
Examples: 

Matrix tree theorem, 
Squaring the square,
Electrician’s  proof of Euler’s formula.

REPLY [3 votes]: I really liked the discussion of electrical circuits in the recent book "Probability on Trees and Networks" by Lyons and Peres. Chapters 2, 4 and 9 seem the most relevant to what you want.