The magnetic critical-current density ({ital J}{sub {ital c}{ital m}}) in the low-field limit (where grains are essentially electromagnetically coupled) is found to increase with film thickness for granular YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} films, which is quite an opposite trend in comparison to the variation of the transport {ital J}{sub {ital c}} ({ital J}{sub {ital c}{ital t}}) with film thickness. To explain the thickness dependence of {ital J}{sub {ital c}{ital m}}, theoretical estimation of the several microstructural parameters, e.g., grain-boundary width, thickness, etc., and their variation with the film thickness is attempted. Though such estimation does provide information regarding the sample characteristics, it cannot throw light on the observed discrepancy between {ital J}{sub {ital c}{ital t}} and {ital J}{sub {ital c}{ital m}} over the entire thickness regime. To accommodate the discrepancy it has been proposed that in addition to the microstructural parameters, the trapping of extra vortex chains---in the case of magnetic measurement---between two oppositely directed current loops is also governing the {ital J}{sub {ital c}{ital m}} significantly. The trapped extra flux varies with film thickness and is smaller in case of thinner films ({lt}25 {mu}m). However, in the thinner regime the geometric factor plays a dominant role in controllingmore » the {ital J}{sub {ital c}{ital t}} while it does not have any influence on {ital J}{sub {ital c}{ital m}}.« less