The voltage–current characteristics of a superconducting coil, made of multifilamentary silver-sheathedBi2Sr2Ca2Cu3O10+&dgr;tape, are investigated. We find that a small ac currentIacsuperimposed on a relatively large dc currentIdccauses a significant increase in the coil dc voltage, approximately proportional toIdc,Iac2,and the ac frequency. We attribute this effect to the nonlinear magnetoresistance of the coil, and discuss its significance in power applications of highTcsuperconducting coils, such as fault current limiters and superconducting magnetic energy storage devices. ©1998 American Institute of Physics.