In a certain series $LCR$ $AC$ circuit, it is found that $X_L=2X_C$ and a phase difference between the current and voltage is $\frac{\pi }{4}$. If now capacitance is made ${\frac{1}{4}}^{th}$ and the inductance and resistance are doubled then which is/are not correct?

In the given circuit the peak voltages across $C, L$ and $R$ are $30 \mathrm{V}, 110 \mathrm{V}$ and $60 \mathrm{V}$ respectively. The rms value of the applied voltage is

The rms value of potential difference $V_0$ shown in figure is

If the input voltage $V_{\mathrm{i}}$ to the circuit below is given by $V_{\mathrm{i}}\left(t\right)=A\cos \left(2\pi ft\right)\text{,}$ the output voltage is given by $V_{\mathrm{o}}\left(t\right)=B\cos \left(2\pi ft+\varphi \right)$.

Which one of the following four graphs best depict the variation of $\varphi$ vs $f$?

An alternating voltage is given by $E=100\sin \left(\omega t+\frac{\pi }{6}\right) \mathrm{V}$. The voltage will be maximum for the first time when time is ($T=$ time period)