$v_r$ = $\frac{1}{2\pi\sqrt{LC}}$ = $\frac{1}{2\times3.14\times\sqrt{3\times27\times10^{-6}}}$ = $\frac{1000}{6.28\times9}$ = 17.7 resonant frequency, $\omega_r$ = $2\pi v_r$ = 2 × 3.14 × 17.7 = 111 rad $\sec^{-1}$ Quality factor in the given resonant circuit Q = $\frac{1}{\text{₹}\sqrt{L/C}}$ = $\frac{1}{7.4}\sqrt{\frac{3}{27\times10^{-6}}}$ = 45 we want to improve the quality factor to twice, without changing resonant frequency (without changing L and C). Q' = 2Q = 90 = $\frac{1}{R'}\sqrt{\frac{L}{C}}$or R' = $\frac{1}{90}\sqrt{\frac{3}{27\times10^{-6}}}$ = 3.7 Ω