Answer
$L_{eq}=L_1+L_2$
Work Step by Step
As $emf_1=L_1\frac{di}{dt}$ and $emf_2=L_2\frac{di}{dt}$;
$emf=emf_1+emf_2$
The above equation can be written as:
$emf=L_1\frac{di}{dt}+L_2\frac{di}{dt}=(L_1+L_2)(\frac{di}{dt})$
From above equation, it is clear that the equivalent inductance is ;
$L_{eq}=L_1+L_2$
