In the circuit shown in the figure, a.c. source gives voltage $$\mathrm{V}=20 \cos (2000 \mathrm{t})$$. Impedance and r.m.s. current respectively will be

Which graph shows the correct variation of r.m.s. current 'I' with frequency 'f' of a.c. in case of (LCR) parallel resonance circuit?

The peak value of an alternating emf '$$\mathrm{e}$$' given by $$\mathrm{e}=\mathrm{e}_0 \cos \omega \mathrm{t}$$ is 10 volt and its frequency is $$50 \mathrm{~Hz}$$. At time $$\mathrm{t}=\frac{1}{600} \mathrm{~s}$$, the instantaneous e.m.f is $$\left(\cos \frac{\pi}{6}=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}\right)$$

A circuit containing resistance R$$_1$$, inductance L$$_1$$ and capacitance C$$_1$$ connected in series resonates at the same frequency 'f$$_0$$' as another circuit containing R$$_2$$, L$$_2$$ and C$$_2$$ in series. If two circuits are connected in series then the new frequency at resonance is