  We consider the full nonequilibrium response of a mesoscopic capacitor in the
large transparency limit, exactly solving a model with electron-electron
interactions appropriate for a cavity in the quantum Hall regime. For a cavity
coupled to the electron reservoir via an ideal point contact, we show that the
response to any time-dependent gate voltage $V_{\rm g}(t)$ is strictly linear
in $V_{\rm g}$. We analyze the charge and current response to a sudden gate
voltage shift, and find that this response is not captured by a simple circuit
analogy. In particular, in the limit of strong interactions a sudden change in
the gate voltage leads to the emission of a sequence of multiple charge pulses,
the width and separation of which are controlled by the charge-relaxation time
$\tau_{\rm c} = h C_{\rm g}/e^2$ and the time of flight $\tau_{\rm f}$. We also
consider the effect of a finite reflection amplitude in the point contact,
which leads to nonlinear-in-gate-voltage corrections to the charge and current
response.
