  We consider a system of non-interacting particles on a line with initial
positions distributed uniformly with density $\rho$ on the negative half-line.
We consider two different models: (i) each particle performs independent
Brownian motion with stochastic resetting to its initial position with rate $r$
and (ii) each particle performs run and tumble motion, and with rate $r$ its
position gets reset to its initial value and simultaneously its velocity gets
randomised. We study the effects of resetting on the distribution $P(Q,t)$ of
the integrated particle current $Q$ up to time $t$ through the origin (from
left to right). We study both the annealed and the quenched current
distributions and in both cases, we find that resetting induces a stationary
limiting distribution of the current at long times. However, we show that the
approach to the stationary state of the current distribution in the annealed
and the quenched cases are drastically different for both models. In the
annealed case, the whole distribution $P_{\rm an}(Q,t)$ approaches its
stationary limit uniformly for all $Q$. In contrast, the quenched distribution
$P_{\rm qu}(Q,t)$ attains its stationary form for $Q<Q_{\rm crit}(t)$, while it
remains time-dependent for $Q > Q_{\rm crit}(t)$. We show that $Q_{\rm
crit}(t)$ increases linearly with $t$ for large $t$. On the scale where $Q \sim
Q_{\rm crit}(t)$, we show that $P_{\rm qu}(Q,t)$ has an unusual large deviation
form with a rate function that has a third-order phase transition at the
critical point. We have computed the associated rate functions analytically for
both models. Using an importance sampling method that allows to probe
probabilities as tiny as $10^{-14000}$, we were able to compute numerically
this non-analytic rate function for the resetting Brownian dynamics and found
excellent agreement with our analytical prediction.
