= Solution
A <voltage> with boundary values $u(a)$ and $u(b)$ is a function $u:V\to\mathbb R$ that is harmonic at every other vertex:
$$
\sum_yc(x,y)(u(x)-u(y))=0,
\qquad x\notin\{a,b\}.
$$
A <current flow> is an antisymmetric function $i(x,y)=-i(y,x)$ satisfying Kirchhoff's node law $\sum_yi(x,y)=0$ away from its source and sink. Voltage and current are related by <Ohm's law>,
$$
i(x,y)=c(x,y)(u(x)-u(y)).
$$
The <effective resistance> is the voltage drop divided by the total current from $a$ to $b$. Equivalently, it is the voltage drop generated by a unit current flow:
$$
R_{\mathrm{eff}}(a,b)=\frac{u(a)-u(b)}{\sum_yi(a,y)}.
$$
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