A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ flow through resistance of $$3\, \Omega$$ and $$2\,\Omega$$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

In a series $$L R$$ circuit $$X_{L}=R$$ and power factor of the circuit is $$P_{1}$$. When capacitor with capacitance $$C$$ such that $$X_{L}=X_{C}$$ is put in series, the power factor becomes $$P_{2}$$. The ratio $$\frac{P_{1}}{P_{2}}$$ is:

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :

To increase the resonant frequency in series LCR circuit,