A unit step voltage is applied at $$t = 0$$ to a series $$RL$$ circuit with zero initial conditions.

In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor

Determine the resonance frequency and the $$Q$$ $$-$$ factor of the circuit shown in Fig.

Data: $$\,\,\,\,\,R = 10\,\Omega ,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C = 3\,\mu F,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L_1} = 40\,mH,\,\,\,\,\,\,\,\,{L_2} = 10\,mH$$
and $$\,\,\,\,\,\,\,\,M = 10\,mH.$$

Resistances $${R_1}$$ and $${R_2}$$ have, respectively, nominal values of $$10\Omega $$ and $$5\Omega ,$$ and tolerances of $$ \pm 5\% $$ and $$ \pm 10\% $$. The range of values for the parallel combination of $${R_1}$$ and $${R_2}$$ is