Calculating the effects of longitudinal resistance in multi-series-connected quantum Hall effect devices

Many ac quantized Hall resistance experiments have measured significant val ues of ac longitudinal resistances under temperature and magnetic field con ditions in which the de longitudinal resistance values were negligible. We investigate the effect of nonvanishing ac longitudinal resistances on measu rements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones report ed previously for de quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devic es. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not ac count for the frequency dependences of the ac quantized Hall resistances re ported in the literature.