As shown in the figure, a current generator I_g delivers a constant current i to the circuit. The wire cd is held fixed, whereas the wire ab is made to slide on the smooth, thick rails with a constant velocity v towards the right. Each of these wires has a resistance r . Determine the current passing through the wire cd .

Step-by-step solution

Let the current passing through the wire cd be i₁ and through the wire ab be i₂ . Both currents flow from the top rail to the bottom rail. According to Kirchhoff's current law, the total current i from the generator splits into the two branches: i = i₁ + i₂ The wire ab moves with a constant velocity v in a uniform magnetic field B directed into the plane of the paper. This induces a motional EMF in the wire ab given by: E = Bvl Using the right-hand rule for v B , the induced EMF is directed from b to a (upwards). T