  Transmission-line waveguides can mediate long-range fluctuation-induced
forces between neutral objects. We present two approaches for the description
of these forces between electric components embedded in transmission-line
circuits. The first, following ordinary quantum electrodynamics (QED), consists
of the quantization and scattering theory of voltage and current waves inside
transmission lines. The second approach relies on a simple circuit analysis
with additional noisy current sources due to resistors in the circuit, as per
the fluctuation-dissipation theorem (FDT). We apply the latter approach to
derive a general formula for the Casimir force induced by circuit fluctuations
between any two impedances. The application of this formula, considering the
sign of the resulting force, is discussed. While both QED and FDT approaches
are equivalent, we conclude that the latter is simpler to generalize and solve.
