Alternating Current

A sinusoidal voltage of peak value 300 V and an angular frequency $\mathrm{\omega }$= 400 rad/s is applied to series L-C-R circuit, in which R = 3 $\mathrm{\Omega }$, L = 20 mH and C = 625 µF. The peak current in the circuit is

• 30$\sqrt{2}$ A

• 60 A

• 100 A

• 60$\sqrt{2}$ A

A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will

• increase exponentially

• decrease exponentially

• decrease linearly

• remain constant

A transformer of 100% efficiency has 200 turns in the primary and 40000 turns in secondary. It is connected to a 220 V main supply and secondary feeds to a 100 k$\mathrm{\Omega }$resistance. The potential difference per turn is

• 1.1 V

• 25 V

• 18 V

• 11 V

A metal wire of linear mass density of 9.8 g/m is stretched with a tension of 10 kg-wt between two rigid supports 1m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency η. The frequency η of the alternating source is 

• 50 Hz

• 100 Hz

• 200 Hz

• 25 Hz

An L-C-R series circuit consists of a resistance of 10 Ω a capacitor of reactance 6.0 Ω and an inductor coil. The circuit is found to resonate when put across a 300 V, 100 Hz supply. The inductance of coil is (take $\mathrm{\pi }$ = 3)

• 0.1 H

• 0.01 H

• 0.2 H

• 0.02 H

In L-R circuit the current increases to three - fourth of its maximum value in 4s, then the time constant of the circuit is

• 2 log_e 2

• $\frac{4}{{\log }_{\mathrm{e}}2}$

• $\frac{2}{{\log }_{\mathrm{e}}2}$

• $\frac{{\log }_{\mathrm{e}}2}{2}$

Power factor of L-C-R circuit in resonation condition is

• 1

• $\frac{1}{2}$

• zero

• $\frac{1}{\sqrt{2}}$

An inductor and a capacitor are connected in an AC circuit inductance and capacitance are 1 H and 25 µF, then for maximum current, angular frequency will be (circuit is connected in series)

• 200 rad/s

• 50 rad/s

• 100 rad/s

• 150 rad/s

A step-up transformer has transformation ratio 3 : 2. The  voltage in the secondary coil, if the voltage in the primary is 30 V will be

• 300 V

• 90 V

• 45 V

• 23 V

In the inductive circuit given in the figure, the current rises after the switch is closed. At instant when the current is 15  mA, then potential difference across the inductor will be

• zero

• 240 V

• 180 V

• 60 V