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A computer-based automatic alternating current (ac) bridge for impedance measurement is proposed. The problem of impedance measurement is formulated as a linear-in-parameter estimation one, and a suitable algorithm is proposed that ensures high measurement accuracy under a high convergence rate. In particular, the optimum experimental conditions regarding the reference resistance and the sampling time are developed. These conditions guarantee that the estimation is performed with possibly high accuracy. This paper also shows how to use the proposed approach for fault detection, which is very important from the point of view of modern control and fault diagnosis. The final part of this paper shows a number of illustrative experiments that justify the effectiveness of the proposed approach.