When AC voltage is applied to an inductor, current lags behind voltage by angle of?

The inductor generates induced electromotive force (EMF) and opposes the changes in the current flow. Due to this the current lag the voltage by 90 degrees.

X_C  = 1/ ωC

On increasing w; XC decreases so Z decreases, current in circuit increases.

$As{V}^2=V_R^2+C_C^2$

$?V_R=\sqrt[]{V^2-V_C^2}=\sqrt[]{{10}^2-8^2}=6V$

$\tan ?\theta =\frac{X_C}{X_R}=\frac{V_C}{V_R}=\frac{8}{6}=\frac{4}{3}$  

Now,

Reactance of the capacitor is $X=\frac{1}{\omega C}$

$C^{\text{'}}=3C$

${\omega }^{\text{'}}=3\omega$

$X^{\text{'}}=\frac{1}{C^{\text{'}}{\omega }^{\text{'}}}=\frac{1}{9\omega C}$

$X^{\text{'}}=\frac{X}{9}$