In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is :

• $\frac{\mathrm{Q}}{2}$

• $\frac{\mathrm{Q}}{\sqrt{2}}$

• $\frac{\mathrm{Q}}{\sqrt{3}}$

• $\frac{\mathrm{Q}}{3}$

An LC circuit is in the state of resonance. If C = 0.1 F and L = 0.25 H, neglecting ohmic resistance of the circuit, what is the frequency of oscillations?

• 1007 Hz

• 100 Hz

• 109 Hz

• 500 Hz

A coil having resistance of 50 ohm and an inductance of 10 ohm, is connected to a 100 volt battery. The energy stored in the coil is

• 10 J

• 20 J

• 30 J

• 40 J

A capacitor when charged by a potential difference of 200 volt, stores a charge of 0.1 C. By discharging, energy liberated by the capacitor is

• -30 J

• -15 J

• 10 J

• 20 J

The core used in transformer and other electromagnetic instruments is laminated, the reason is

• to increase the electric field

• to increase the magnetic field

• to reduce the loss of energy due to eddy currents

• to decrease the resistance

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