Answer
a) stay the same
b) decrease
Work Step by Step
(a) We know that the resonance frequency is given as $\omega=\frac{1}{\sqrt{LC}}$. This equation shows that the resistance has nothing to do with the resonance frequency. Thus, the resonance frequency will stay the same, even if the resistance is doubled.
(b) We know that current and resistance are inversely proportional; that is, $I=\frac{V}{Z}=\frac{V}{R^2+(X_L-X_c)^2}$. Thus, when the resistance is doubled, the current will decrease.
