  We compare time variations of the H$\alpha$ and X-ray emissions observed
during the pre-impulsive and impulsive phases of the C1.1-class solar flare on
21 June 2013 with those of plasma parameters and synthesized X-ray emission
from a one-dimensional hydro-dynamic numerical model of the flare. The
numerical model was calculated assuming that the external energy is delivered
to the flaring loop by non-thermal electrons. The H$\alpha$ spectra and images
were obtained using the Multi-channel Subtractive Double Pass spectrograph with
a time resolution of 50~ms. The X-ray fluxes and spectra were recorded by the
Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). Pre-flare
geometric and thermodynamic parameters of the model and the delivered energy
were estimated using RHESSI data.
  The time variations of the X-ray light curves in various energy bands and the
those of the H$\alpha$ intensities and line profiles were well correlated. The
time scales of the observed variations agree with the calculated variations of
the plasma parameters in the flaring loop footpoints, reflecting the time
variations of the vertical extent of the energy deposition layer. Our result
shows that the fast time variations of the H$\alpha$ emission of the flaring
kernels can be explained by momentary changes of the deposited energy flux and
the variations of the penetration depths of the non-thermal electrons.
