A circuit with a resistor, inductor and capacitor in series is resonant at $${f_0}\,\,Hz.$$ If all the component values are now doubled, the new resonant frequency is

In the circuit shown in Fig. $$X$$ $$-$$ is an element which always absorbs power. During a particular operation, it sets up a current of $$1$$ $$amp$$ in the direction shown and absorbs a power $${P_{x}}.$$ It is possible that $$X$$ can absorb the same power $${P_x}$$ for another current $$i.$$ Then the value of this current is

A series $$R-L-C$$ circuit has the following parameter values:
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circuit at resonance is

In the circuit of Figure, Ammeter $${A_2}$$ reads $$12$$ $$A$$ and $${A_3}$$ reads $$9$$ $$A.$$ $${A_1}$$ will read ______