List of top Power Systems Questions on Voltage and Frequency control

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).

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).

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). \[ \vec{H}(r, \theta, \phi) = \frac{1}{r^3} \big( \hat{r} P \cos \theta + \hat{\theta} \sin \theta \big) \]

In the \( (x, y, z) \) coordinate system, three point charges \( Q \), \( Q \), and \( \alpha Q \) are located in free space at \( (-1, 0, 0) \), \( (1, 0, 0) \), and \( (0, -1, 0) \), respectively. The value of \( \alpha \) for the electric field to be zero at \( (0, 0.5, 0) \) 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).
In the \( (x, y, z) \) coordinate system, three point charges \( Q \), \( Q \), and \( \alpha Q \) are located in free space at \( (-1, 0, 0) \), \( (1, 0, 0) \), and \( (0, -1, 0) \), respectively. The value of \( \alpha \) for the electric field to be zero at \( (0, 0.5, 0) \) is \_\_\_\_\_\_ (rounded off to 1 decimal place).
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). \[ \vec{H}(r, \theta, \phi) = \frac{1}{r^3} \big( \hat{r} P \cos \theta + \hat{\theta} \sin \theta \big) \]
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).