In this paper, the problem of electromagnetic transmission via slits in a cavity inside a conducting screen of finite thickness has been considered in the case that the transverse electric(to the slit axis) polarized plane wave is incident on a slit. The problem is solved numerically by the method of moments and the results are compared with those obtained from an equivalent circuit suitable for a case in which the slit width is infinite and the structure is modified to the two partially overlapped conducting planes. It is observed that when the cavity is resonated, the effective slit width reaches its maximum value of $1/pi$ wavelengths, irrespective of the actual slit width and the incidence angle. When the thickness of the conducting plane is much smaller than the wavelength, the numerical results for the effective slit width(or transmission width) agree well with those obtained from the equivalent circuit, even though the slit is as narrow as the thickness of the conducting plane.