A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k$$\Omega$$, an inductor of inductive reactance X_L = 250 $$\pi$$$$\Omega$$ and an unknown capacitor. The value of capacitance to maximize the average power should be : (Take $$\pi$$² = 10)

A 100$$\Omega$$ resistance, a 0.1 $$\mu$$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

A 0.07 H inductor and a 12$$\Omega$$ resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $$\pi$$ as $${{22} \over 7}$$]

A 10 $$\Omega$$ resistance is connected across 220V $$-$$ 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :