The quantum metrological triangle experiment, which is under development at the Bureau National de Métrologie-Laboratoire Central des Industries Électriques (BNM-LCIE), consists of applying Ohm's law directly to the quantities related to the single-electron tunnelling (SET) effect, the ac Josephson effect (JE) and the quantum Hall effect (QHE). The goal of this experiment is to test, at a significant level of uncertainty of about 1 part in 10⁸, the coherence of the constants involved in these three quantum phenomena: the Josephson constant K_J, expected to correspond to the ratio 2e/h (where e is the elementary charge and h the Planck constant); the von Klitzing constant R_K, in relation to the quantum resistance h/e²; and a new constant Q_X, defined here as the estimate of e. Moreover, realization of the metrological triangle experiment, combined with the experiment being developed at the NIST aimed at charging a capacitor by means of a SET pump, will give information liable to be taken into account in future adjustments of the fundamental constants without requiring any hypothesis regarding the physical phenomena involved. The combination of these two experiments should yield a new value of R_K in ohms of the International System of Units (SI). The broad outlines of our experimental set-up are given, along with the expected uncertainties in both the short and long terms.