There are two solenoids of same length and inductance $L$ but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series.<br />$\left( {\rm{1}} \right)$ They are connected in series but separated by large distance,<br />$\left( {\rm{2}} \right)$ they are connected in series with one inside the other and senses of the turns coinciding,<br />$\left( {\rm{3}} \right)$ both are connected in series with one inside the other with senses of the turns opposite as depicted in figures<br />${\rm{1, 2 and 3}}$ respectively. The total inductance of the solenoids in each of the case ${\rm{1, 2 and 3}}$ are respectively<br />.