Starting with the plane-wave solution for scattering from a two-layer sphere, the quasistatic response of a thin conducting shell is recovered analytically. Responses are also computed for shells of arbitrary thickness, and the range of validity of the thin-shell approximation is determined. These results are extended to the time domain by a numerical inverse Fourier transform which yields the response to a step-function incident field (magnetic or electric). It is found that under the thin-shell approximation, the transient response has a simple single-exponential form. This is modified to some extent when the arbitrary thickness of the shell is allowed for.