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 $$\left(\tan 60^{\circ}=\sqrt{3}\right)$$

Resistor of $$2\Omega$$, inductor of $$100 \mu \mathrm{H}$$ and capacitor of $$400 \mathrm{pF}$$ are connected in series across a source of $$\mathrm{e}_{\mathrm{rms}}=0.1$$ Volt. At resonance, voltage drop across inductor is

In the given circuit, r.m.s. value of current through the resistor $$\mathrm{R}$$ is

In the given circuit, if $$\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / \mathrm{s}$$ then the value of $$\left(V_A-V_B\right)$$ at this instance will be