The image shows a circuit with a resistor and inductor in series, connected to an AC voltage source. The question asks for the unknown quantity X, which is likely the impedance (Z) of the circuit.

Impedance is the total opposition to current flow in an AC circuit. For a series RL circuit, it is calculated using the formula:

$Z=\sqrt{R^2+{\left(\omega L\right)}^2}$

where R is resistance, ω is angular frequency, and L is inductance. The correct option is the one that represents this formula.

Final answer: The first option, $\sqrt{R^2+{\left(\omega L\right)}^2}$