With increase in frequency of a.c. supply, the impedance of an L-C-R series circuit

In an a.c. circuit the instantaneous current and emf are represented as $$\mathrm{I}=\mathrm{I}_0, \sin [\omega \mathrm{t}-\pi / 6]$$ and $$\mathrm{E}=\mathrm{E}_0 \sin [\omega \mathrm{t}+\pi / 3]$$ respectively. The voltage leads the current by

When an inductor '$$L$$' and a resistor '$$R$$' in series are connected across a $$15 \mathrm{~V}, 50 \mathrm{~Hz}$$ a.c. supply, a current of $$0.3 \mathrm{~A}$$ flows in the circuit. The current differs in phase from applied voltage by $$\left(\frac{\pi}{3}\right)^c$$. The value of '$$R$$' is $$\left(\sin \frac{\pi}{6}=\cos \frac{\pi}{3}=\frac{1}{2}, \sin \frac{\pi}{3}=\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}\right)$$

An a.c. source of $$15 \mathrm{~V}, 50 \mathrm{~Hz}$$ is connected across an inductor (L) and resistance (R) in series R.M.S. current of $$0.5 \mathrm{~A}$$ flows in the circuit. The phase difference between applied voltage and current is $$\left(\frac{\pi}{3}\right)$$ radian. The value of resistance $$(\mathrm{R})$$ is $$\left(\tan 60^{\circ}=\sqrt{3}\right)$$