Condition for current to be in phase with emf

In a series $RLC$ circuit, current is in phase with the applied emf at resonance.

So, the impedance is purely resistive: $Z = R = 20\,\Omega$

Given source voltage

The given ac source is $220\,\text{V}$, which is the rms voltage.

Hence, $V_{\text{rms}} = 220\,\text{V}$

Find rms current

Using Ohm’s law for AC at resonance: $I_{\text{rms}} = \frac{V_{\text{rms}}}{R} = \frac{220}{20} = 11\,\text{A}$

Find amplitude (peak) current

Amplitude of current is: $I_0 = \sqrt{2}\, I_{\text{rms}} = \sqrt{2}\times 11 = 11\sqrt{2}\,\text{A}$

Given that amplitude is $\sqrt{x}$ A, so $\sqrt{x} = 11\sqrt{2}$

Compute $x$

Squaring both sides: $x = (11\sqrt{2})^2 = 121 \times 2 = 242$

Answer check

Derived answer: $242$

Stored correct answer: $242$

They match.