La0.8Sr0.2MnO$_3$−$\delta$ (LSM)/8 mol% yttria-stabilized ZrO$_2$ (YSZ) (LSM/YSZ) composite cathodes with varying composition are studied for both polarization and ohmic resistance by electrochemical impedance spectroscopy. It was found that total resistance and polarization resistance are lowest for the composite with 60 wt% of LSM (LSM60/YSZ40). However, the ohmic resistance was highest for the same composition and amounted to 60% of the total resistance value. Compositional dependence of resistances has been explained based on the variations of the triple phase boundaries and width of the O$_2$−ion migration path with the composition of the electrode. Based on the observed area specific ohmic resistance values for the composite cathodes, it is proposed to verify the advantages of LSM/YSZ over LSM cathode in anode-supported solidoxide fuel cell with thin electrolyte.