We present a set of experimental results concerning the power spectrum of current noise, detected on a granular high Tc superconductor submitted either to a slowly varying magnetic field or to a varying current intensity. Experiments were performed on a YBCO specimen suitably treated in order to weaken the weak links without affecting the oxygen content of grains. The weakening of the intergrain region allowed the use of very small magnetic fields and currents to induce the resistive transition of the specimen and to observe current noise. The induced noise is of the 1/f2 type and will be interpreted in terms of two different models. One of the model is based on the enhancement of the noise due to the clustering of the resistive transition of the weak links, produced by correlation effects related to the strong nonlinearity of their Josephson type I-V characteristics. This model has been the object of a computer simulation based on a 3D-network of Josephson-like elements and seems suitable to explain the noise produced by current variation. The second model explains the excess noise as produced by discontinuous penetration of the magnetic flux inside the intergrain region. This discontinuity is related to the field screening effect of rings made of several superconducting weak links connecting different grains, which are alternatively broken and restored by the current induced during flux variation, and seems suitable to explain the larger noise produced by a varying magnetic field.