A series combination of resistor of resistance 100Ω inductor of...

The formula to calculate the quality factor of an LCR circuit is given by

$Q = \dfrac{1}{R}\sqrt{\dfrac{L}{C}} . . . \left(1\right)$

Substitute the values of the known parameters into equation (1) to calculate the required quality factor of the circuit.

$\begin{cases}Q & = & \dfrac{1}{100}\sqrt{\dfrac{1}{6 . 25 \times {10}^{- 6}}} \\ & = & \dfrac{1}{100} \times \dfrac{1000}{2 . 5} \\ & = & 4\end{cases}$