Calculating current in a dc circuit
Well, apparently it is a bridge configuration, but one of the diagonals is shorted, therefore \$R_3\$ ends up in parallel with \$R_1\$ and \$R_4\$ ends up in parallel with \$R_2\$.

If you redraw the schematic you'll see that \$R_3 \parallel R_1\$ and \$ R_1 \parallel R_4\$ are in series with the current generator, therefore if the resistances and \$I_g\$ are known, it is easy to compute the voltage across each resistor and therefore the current in each.

Knowing the current in each resistor then lets you calculate \$I\$ applying KCL.