  An important goal of current and future long baseline neutrino oscillation
experiments pertains to determination of the Dirac-type leptonic $CP$ phase,
$\delta_{13}$. We consider the new physics scenario of an eV scale sterile
neutrino along with three active neutrinos and demonstrate the impact on the
$CP$ and $T$ violation measurements in neutrino oscillations. We address the
question of disentangling the intrinsic effects from extrinsic effects in the
standard three neutrino paradigm as well as the scenario with added light
sterile neutrino. We define a metric to isolate the two kinds of effects and
our approach is general in the sense that it is independent of the choice of
$\delta_{13}$. We study the role of different appearance and disappearance
channels which can contribute to CP and T violation measurements. We perform
the analysis for different long baseline experiments which have different
detection capabilities such as Water Cherenkov (WC) and Liquid Argon Time
Projection Chamber (LArTPC).
