If the energy of a continuous-time signal \( x(t) \) is \( E \) and the energy of the signal \( 2x(2t - 1) \) is \( cE \), then \( c \) is (rounded off to 1 decimal place).
A 3-phase star connected slip ring induction motor has the following parameters referred to the stator: \[ R_s = 3 \, \Omega, \, X_s = 2 \, \Omega, \, X_r' = 2 \, \Omega, \, R_r' = 2.5 \, \Omega \] The per phase stator to rotor effective turns ratio is 3:1. The rotor winding is also star connected. The magnetizing reactance and core loss of the motor can be neglected. To have maximum torque at starting, the value of the extra resistance in ohms (referred to the rotor side) to be connected in series with each phase of the rotor winding is ___________ (rounded off to 2 decimal places).
The given equation represents a magnetic field strength \( \vec{H}(r, \theta, \phi) \) in the spherical coordinate system, in free space. Here, \( \hat{r} \) and \( \hat{\theta} \) represent the unit vectors along \( r \) and \( \theta \), respectively. The value of \( P \) in the equation should be (rounded off to the nearest integer). \[ \vec{H}(r, \theta, \phi) = \frac{1}{r^3} \big( \hat{r} P \cos \theta + \hat{\theta} \sin \theta \big) \]