A series combination of resistor of resistance 100   Ω inductor of inductance 1   H and…

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

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

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

$\begin{array}{rcl}Q& =& \frac{1}{100}\sqrt{\frac{1}{6.25\times {10}^{-6}}}\\ & =& \frac{1}{100}\times \frac{1000}{2.5}\\ & =& 4\end{array}$