AC measurements of the quantized Hall resistance

The quantized Hall resistance R_H(i), for i=2, 4 and 6 has been measured over the frequency range from dc to 3 kHz using a standard four terminal-pair impedance bridge. For the ith plateau we found that R_H(i) depended linearly on the magnetic flux density B and quadratically on the frequency f. That is, the relative difference ΔR_H(i,f)/R_H(i) between the ac and dc values is consistent with the empirical relationship k(i)Bf² , where k(i) is constant. Below 3 kHz k(i) decreases by approximately a factor of six as i increases from 2 to 6. These results are consistent with inductances ≈100 μH, which depend on B, in series with each terminal of the quantum Hall device. From dc to 3 kHz we can derive the ac value of a standard resistor in terms of R_H (2) with a type A relative uncertainty (1σ) of 0.05×10 ^-6 f² when f is expressed in kHz