In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the...

Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the...

Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically...

The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...

A device that transforms voltages from one value to another using induction is called a transformer. A transformer consists of two separate coils, or windings, wrapped around the same soft iron core. However, they are electrically insulated from each other.
The iron core has a substantial relative permeability. Therefore, the magnetic field lines generated due to the current in one winding are almost entirely confined within the core, such that the same magnetic flux permeates each turn of both...

Rolling resistance, also known as rolling friction, is the force that resists the motion of a rolling object, such as a wheel, tire, or ball, when it moves over a surface. It is caused by the deformation of the object and the surface in contact with each other, as well as other factors like internal friction, hysteresis, and energy losses within the materials. Rolling resistance opposes the object's motion, requiring additional energy to overcome it and maintain movement. In practical...