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

A $$100$$ $$\mu A$$ ammeter has an internal resistance of $$100\,\Omega $$. For extending its range to measure $$500$$ $$\mu A$$, the shunt required is of resistance (in $$\Omega $$)