Answer:
7/25
Step-by-step explanation:
In a circuit with parallel inductors of 2 H, 7H, and 4 H, you want to know the fraction of total current that flows in the 4 H inductor.
Admittance
The current in parallel circuit branches is proportional to the admittance of the branch. Since all of the circuit elements here are inductors, we can do the math as though the admittance were real instead of complex.
The desired ratio is ...
(1/4)/(1/4 +1/7 +1/2) = (1/4)/((7 +4 +14)/28) = 7/25
The current in the 4 H inductor is 7/25 of the total circuit current.