A galvanometer of resistance 100 Ω is converted to a voltmeter of range 10 V by connecting a resistance of 10 kΩ. The resistance required to convert the same galvanometer to an ammeter of range 1 A is

• 0.4 Ω

• 0.3 Ω

• 0.1 Ω

• 0.2 Ω

Two wires with currents 2 A and 1 A are enclosed in a circular loop. Another wire with current 3 A is situated outside the loop as shown. Then $\oint \overrightarrow{\mathrm{B}} . \overrightarrow{\mathrm{dl}}$ around the loop is

• µ₀

• 3 µ₀

• 6 µ₀

• 2 µ₀

An L-C-R series AC circuit is at resonance with 10 V each across L, C and R. If the resistance is halved, the respective voltages across L, C and R are

• 10 V, 10 V and 5 V

• 10 V, 10 V and 10 V

• 20 V, 20 V and 5 V

• 20 V,20 V and 1O V

A 5O Hz AC current of peak value 2 A flows through one of the pair of coils. If the mutual inductance between the pair of coils is 150 mH, then the peak value of voltage induced in the second coil is

• $30 \mathrm{\pi V}$

• $60 \mathrm{\pi V}$

• $15 \mathrm{\pi V}$

• $300 \mathrm{\pi V}$

A transformer is used to light a 100 W and 110 V lamp from a 220 V main supply. If the main current is 0.5 A, then the efficiency of the transformer is nearly

• 89 %

• 100 %

• 91 %

• 85 %

An L-C-R series circuit is at resonance. Then

• the phase difference between current and voltage is 90°

• the phase difference between current and voltage is 45°

• its impedance is purely resistive

• its impedance is zero

A 100 W bulb produces an electric field of 2.9 Vm^-1 at a point 3 m away. If the bulb is replaced by 400 W bulb without distributing other conditions, then the electric field produced at the same point is

• 2.9 Vm^-1

• 3.5 Vm^-1

• 5 Vm^-1

• 5.8 Vm^-1

In the total electromagnetic energy falling on a surface is U, then the total momentum delivered (for complete absorption) is

• $\frac{\mathrm{U}}{\mathrm{c}}$

• cU

• $\frac{\mathrm{U}}{{\mathrm{c}}^2}$

• c²U

In the given circuit the current through the battery is

• 0.5 A

• 1 A

• 1.5 A

• 2 A

50.

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres ${\mathrm{\sigma }}_1/{\mathrm{\sigma }}_2$ is

• R₁ / R₂

• R₂ / R₁

• $\sqrt{\left({\mathrm{R}}_1 / {\mathrm{R}}_2\right)}$

• R₁² / R₂²