Adding small AC signal to a DC current using inductive coupling
First, there will be just one current in the circuit you show. The current into the coil must be the same as the current out of the cell.

You can do pretty much exactly what you have drawn. Use a transformer with the secondary winding connected as shown, in series with your dc source. You can use a function generator or other sine wave source connected to the primary winding of the transformer.

You will need to select a transformer designed to work at the ripple frequency of interest. If you want your ripple to be at the mains frequency this should be easy.