The conservation of magnetic helicity, K= integral A.B d3x, determines whether tearing activity increases or decreases the net plasma current I in a tokamak. A centrally peaked distribution of current is shown to lose current during a relaxation and a hollow distribution to gain current, the change can be approximately=20% of the total current. Tearing activity relaxes the current distribution j/sub ////B towards a spatial constant kT=((Vb integral d psi )+( integral eta ckad psi ))/( integral eta cd psi ) with Vb the applied loop voltage, ka( psi ) the distribution of the bootstrap and driven currents, eta c the resistivity coefficient and psi the toroidal flux. It is the resistivity weighting of kT that accounts for the change in the net plasma current I.