An a.c. source of angular frequency '$$\omega$$' is fed across a resistor '$$R$$' and a capacitor '$$C$$' in series. The current registered is I. If now the frequency of source is changed to $$\frac{\omega}{3}$$ (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency '$$\omega$$' will be

In an a.c. circuit, a resistance R = 40 $$\Omega$$ and an inductance 'L' are connected in series. If the phase angle between voltage and current is 45$$^\circ$$, then the value of the inductive reactance is (tan 45$$^\circ$$ = 1)

The frequency of the output signal of an LC oscillator circuit is '$$\mathrm{F}$$' Hz with a capacitance of 0.1 $$\mu \mathrm{F}$$. If the value of the capacitor is increased to $$0.2~ \mu \mathrm{F}$$, then the frequency of the output signal will be

In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are