A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03 Ω/phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is ______.

Two semi-infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y< 0) and region 2 (y>0) are 2 and 5, respectively. Region 1 has uniform electric field $$\overrightarrow E=3{\widehat a}_x\;+\;4{\widehat a}_y\;+\;2{\widehat a}_z$$, where $${\widehat a}_x$$, $${\widehat a}_y$$, and $${\widehat a}_Z$$ are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is

Match the following.

A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of μ0 is $$4\mathrm\pi\times10^{-7}$$ in SI unit. If a uniform magnetic field intensity $$\overrightarrow H=10^7\;\widehat z\;A/m$$ is applied, then the peak value of the induced voltage, V_turn ( in Volts), is _________.