Who can solve this?

My answer : - . 8 I ₀

Let " I ₁ " denote the current flowing through the upper part of the shown circuit and " I ₂ " , the current flowing through the lower part . Let " I ₃ " denote the current flowing through the switch .

Just before the switch was closed , we had : -

I ₁ = I ₀ , I ₂ = I ₀ ;

I ₁ + I ₂ = 2 I ₀

Since , an inductor provides theoretically infinite resistance just after the switch is closed , we still have the sum of these currents unaltered .

The voltage drop across the toroid just after the switch is closed , is : -

V = R I ₃ - U

Now we apply Kirchoff ' s Voltage Rule for the whole circuit and the upper part of the circuit respectively .

R I ₁ + 2 V = U

R ( I ₁ + I ₃ ) = V + 2 U

Also applying Kirchoff ' s Junction Rule , we have : -

I ₁ = I ₂ + I ₃

Finally , the total set of available equations is : -

I ₁ + I ₂ = 2 I ₀

Yes your answer is correct. But its too late now, I already solved the question [3]