thermodynamics - Joule Thomson Coefficient derivation

In deriving Joule Thomson effect coefficient, why do we take $dH=0$ and also why do we take $H$ as a function of $T$ and $P$ only and not $V$? i.e. why do we take $$(\partial H/ \partial T)dT+(\partial H/\partial P)dP=0$$ and not

$$(\partial H/\partial T)dT+(\partial H/\partial P)dP+(\partial H/\partial V)dV=0$$

Any links would also be appreciated.

Thanks.