Impedance of Finite Length Resistor

We determine the impedance of a cylindrical metal tube (resistor) of radius a, length g, and conductivity σ, attached at each end to perfect conductors of semi-infinite length. Our main interest is in the asymptotic behavior of the impedance at high frequency,, k >> 1/a . In the equilibrium regime, ka²<< g, the impedance per unit length is accurately described by the well-known result for an infinite length tube with conductivity σ . In the transient regime, ka²>> g, we derive analytic expressions for the impedance and wakefield.