A 240 V d.c. shunt motor with an armature resistance of 0.5 $$\Omega$$ has a full load current of 40 A. Find the ratio of the stalling torque to the full load torque when a resistance of 1 $$\Omega$$ is connected in series with the armature?

A 3-phase squirrel cage induction motor has a full load efficiency of 0.8 and a maximum efficiency of 0.9. It is operated at a slip of 0.6 by applying a reduced voltage. The efficiency of the motor at this operating point is:

An infinite number of charges, each equal to $$'q'$$ are placed along the $$x=1,x=2, x=4, x=8, x=16$$ and so on, Find the potential and electric field at point $$x=0,$$ due to these system of charges.

An electron moves in the $$X$$-$$Y$$ plane with a speed of $${10^6}\,\,m/s.$$ Its velocity vector makes an angle of $${60^ \circ }$$ with $$X$$ axis. A magnetic field of magnitude $${10^{ - 2}}T$$ exists along the $$Y$$ axis. Compute the magnetic force exerted on the electron and its direction.