We demonstrate that nuclear spin fluctuations lead to the electric current noise in the mesoscopic samples of organic semiconductors showing the pronounced magnetoresistance in weak fields. For the bipolaron and electron-hole mechanisms of organic magnetoresistance, the current noise spectrum consists of the high frequency peak related to the nuclear spin precession in the Knight field of the charge carriers and the low frequency peak related to the nuclear spin relaxation. The shape of the spectrum depends on the external magnetic and radiofrequency fields, which allows one to prove the role of nuclei in magnetoresistance experimentally.
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