$$ \omega = \frac{1}{\sqrt{LC}} $$

For a series LCR circuit, the maximum current occurs at resonance, where the inductive reactance equals the capacitive reactance. Given the values:

Inductance: $$ L = 100 \, \text{mH} = 0.1 \, \text{H} $$

Capacitance: $$ C = 25 \, \text{nF} = 25 \times 10^{-9} \, \text{F} $$

we first calculate the product $$ LC $$:

$$ LC = 0.1 \times 25 \times 10^{-9} = 2.5 \times 10^{-9} $$

Next, compute the square root of the product:

$$ \sqrt{LC} = \sqrt{2.5 \times 10^{-9}} $$

Recognize that:

$$ \sqrt{2.5 \times 10^{-9}} = \sqrt{2.5} \times \sqrt{10^{-9}} \approx 1.581 \times 10^{-4.5} $$

Since $$ 10^{-4.5} = 3.162 \times 10^{-5} $$, we have:

$$ \sqrt{LC} \approx 1.581 \times 3.162 \times 10^{-5} \approx 5.0 \times 10^{-5} $$

Now, the angular frequency at resonance becomes:

$$ \omega = \frac{1}{5.0 \times 10^{-5}} = 2.0 \times 10^{4} \, \text{radians/s} $$

Thus, the angular frequency of the AC source for maximum current in the circuit is:

$$ \omega = 2 \times 10^4 \, \text{radians/s} $$