In this paper, the problem of electromagnetic transmission via slits in a cavity inside conducting screen of finite thickness is considered for the case that the TE(to the slit axis) polarized plane wave is incident on the slit in conducting screen. Using the method of moments the variations of the transmitted power through the slits are obtained and compared with those computed from an equivalent circuit constructed using an equivalent slit admittance. It is found that the effective slit width of a narrow slit, at resonance, becomes $1/{pi}$ wavelengths independently of the actual slit width. The transmission resonance phenomena in the proposed geometry are explained in connection with the variations of an equivalent admittance of the slit in the cavity.