The effective current I in the given circuit at very high frequencies will be _____ A .

At very high frequencies, inductor acts as an open circuit and capacitor as short circuit.

So, capacitive reactance, $X_C=\frac{1}{\omega C}\approx 0$

Also, inductive reactance, $X_L=\omega L\approx \infty$

Thus, equivalent circuit can be redrawn as

Here, both $4 \mathrm{\Omega }$ resistances are in parallel and together they are in series with$1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ resistances.

Equivalent impedance is $Z=1+\frac{4\times 4}{4+4}+2=5 \mathrm{\Omega }$

Effective current is $I=\frac{220 \mathrm{V}}{5 \mathrm{\Omega }}=44 \mathrm{A}$