31.

In Wheatstone network, P = 2 Ω, Q = 2 Ω, R = 2 Ω and S = 3 Ω. The resistance with which S is to be shunted in order that the bridge may be balanced is

• 4 Ω

• 1 Ω

• 6 Ω

• 2 Ω

Core of electromagnets are made of ferromagnetic material which has

• low permeability and high retentivity

• high permeability and low retentivity

• low permeability and low retentivity

• high permeability and high retentivity

Two parallel wires 1 m apart carry currents of 1 A and 3 A respectively in opposite directions. The force per unit length acting between two wires is

• 6 × 10^-5 Nm^-1 repulsive

• 6 × 10^-7 Nm^-1 repulsive

• 6 × 10^-5 Nm^-1 attractive

• 6 × 10^-7 Nm^-1 attractive

A galvanometer of resistance 50 Ω gives a full scale deflection for a current 5 x 10^-4 A. The resistance that should be connected in series with the galvanometer to read 3 V is

• 5059 Ω

• 595 Ω

• 5950 Ω

• 5050 Ω

A cyclotron is used to accelerate

• only negatively charged particles

• neutron

• both positively and negatively charged particles

• only positively charged particles

A transformeris used to light 100 W -110 V lamp from 220 V mains. If the main current is 0.5 A, the efficiency of the transformer is

• 96 %

• 90 %

• 99 %

• 95 %

In an L-C-R circuit, at resonance

• the current is minimum

• the current and voltage are in phase

• the current leads the voltage by $\frac{\mathrm{\pi }}{2}$

• the impedance is maximum

An aircraft with a wingspan of 40 m flies with a speed of 1080 km/h in the Eastward direction at a constant altitude in the Northern  hemisphere, where the vertical component of the Earth's magnetic field is 1.75 × 10^-5 T. Then the emf developed between the tips of the wings is

• 0.21 V

• 0.5 V

• 2.1 V

• 0.34 V

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation I = i_m sin ωt, where i_m = 10 A and ω = 100 rad s^-1. The maximum value of the emf induced in the second coil is

• $\mathrm{\pi }$

• $2\mathrm{\pi }$

• $4\mathrm{\pi }$

• $5\mathrm{\pi }$

The magnetic susceptibility of a paramagnetic material at -73°C is 0.0075 and its value at − 173°C will be

• 0.015

• 0.0045

• 0.0075

• 0.0030