QUESTION 7: TRANSFORMERS 7.1 A three-phase staridella-connecled transformer has 200 turns per phase on the primary windings and 30 turns per phase on the secondary windings. 7.1.1 Caloulate the secondary line voltage if the primary is connectod to a 380 V three-phase supply. (5) 7.12 What current can this transformer deliver if it is rated at 30 kVA ? (2) 7.2 Explain the operaling principle of transformers (3) [10] UESTION 8: DC MACHINES Explain how an EMF can be induced in a straight piece of copper wiro (generator principle). (3) 2 Explain the motor principle. (3) Indicate what type of DC motor will best suit the following requirements: 8.3.1 A hoist or lift that must accelerate from standstill 8.3.2 A fan that runs continuously at a constant speed 8.3.3 An application where the load varies and it is important to keep the speed constant \[ (3 \times 1) \] What visual evidence will immediafely tell you if a motor armature is lap wound?

Below are complete answers for all parts of the questions. ───────────────────────────── QUESTION 7: TRANSFORMERS ───────────────────────────── 7.1 The transformer has 200 turns per phase on the star‐connected primary and 30 turns per phase on the secondary. In a star connection the line voltage (Vₗ) is related to the phase voltage (Vₚ) by   Vₚ = Vₗ/√3 Since the primary is supplied with a 380 V three‐phase line voltage, its phase voltage is   Vₚ(primary) = 380 V / √3 ≈ 219.4 V The transformer’s voltage ratio is   (V secondary phase) / (V primary phase) = (N secondary) / (N primary) = 30/200 = 0.15 Thus, the phase voltage on the secondary winding is   Vₚ(secondary) = 0.15 × 219.4 V ≈ 32.91 V Now, note that if the secondary winding is connected in delta, then the line voltage on the secondary is the same as the phase voltage. (In a delta connection, Vₗ = Vₚ.) Therefore, the secondary line voltage is approximately   Vₗ(secondary) ≈ 32.91 V However, another common interpretation is that the given “200 turns per phase” and “30 turns per phase” imply that the ratio applies to the “phase winding voltages” while the 380 V is the star (line) voltage. Then the voltage transformation step–down from primary phase voltage to secondary phase voltage is 0.15. When the secondary is connected in delta the phase and line voltages are equal so you obtain about 32.9 V line voltage. (If the transformer were star/star connected, the secondary line voltage would be Vₗ(second) = √3 • Vₚ(second) ≈ 57 V. Thus it is important to note the connection type on both sides. Here the term “staridella‐connected” is taken to mean that the primary is star and the secondary is delta.) Answer 7.1.1: Assuming the secondary is delta connected (as “staridella” usually indicates star primary/delta secondary), the secondary line voltage is approximately 32.9 V. ───────────────────────────── 7.1.2 Transformer Rating – Current Delivery The transformer is rated at 30 kVA. For a three‐phase transformer the apparent power is given by   S = √3 × Vₗ × Iₗ Assuming we are considering the secondary side (with Vₗ ≅ 32.9 V):   Iₗ = S / (√3 × Vₗ)     = 30,000 VA / (1.732 × 32.9 V)     ≈ 30,000 / 56.99     ≈ 526 A Thus, the transformer is capable of delivering approximately 526 A on the secondary side. ───────────────────────────── 7.2 Operating Principle of Transformers A transformer works on the principle of electromagnetic induction. When an alternating current flows in the primary winding, it produces a time-varying magnetic flux in the core. This changing magnetic flux links with the secondary winding and, according to Faraday’s law of electromagnetic induction, an electromotive force (EMF) is induced in the secondary winding. The ratio of the voltages in the primary and secondary windings is equal to the ratio of the number of turns in each winding. Ideally, apart from losses (which are small in a good transformer), the power (apparent power) is transferred from the primary to the secondary winding with minimal loss. ───────────────────────────── QUESTION 8: DC MACHINES ───────────────────────────── 8.1 Inducing an EMF in a Straight Copper Wire (Generator Principle) When a straight copper wire moves in a magnetic field, the free electrons in the wire experience a Lorentz force because of their motion perpendicular to the magnetic field. This force causes the electrons to drift toward one end of the wire, thereby creating a separation of charge. This separation sets up an electric potential difference (or EMF) across the ends of the conductor. The magnitude of this induced EMF is proportional to the strength of the magnetic field, the length of the conductor, and the velocity of the conductor perpendicular to the magnetic field. 8.2 The Motor Principle The motor principle is essentially the reverse of the generator principle. When a current flows through a conductor placed in a magnetic field, the conductor experiences a force (again given by the Lorentz force law). In a motor, the force on current-carrying conductors arranged on the rotor produces a torque that causes the rotor to turn. Thus, electrical energy is converted into mechanical energy. 8.3 Selection of DC Motor Types for Specific Applications 8.3.1 A hoist or lift that must accelerate from standstill   – A Series-wound DC motor. Reason: Series motors provide very high starting torque, which is ideal for applications that require rapid acceleration from rest. 8.3.2 A fan that runs continuously at a constant speed   – A Shunt-wound DC motor. Reason: Shunt motors have a nearly constant speed under varying load conditions, making them well suited for continuous operation at a steady speed. 8.3.3 An application where the load varies and it is important to keep the speed constant   – A Compound-wound DC motor. Reason: Compound motors combine the high starting torque characteristics of series windings with the good speed regulation of shunt windings, thus maintaining a more constant speed even when the load varies. 8.4 Visual Evidence of a Lap-Wound Armature If you inspect a DC motor armature that is lap wound, you would notice that:   – The coils are connected in such a way that the end of one coil is connected to the beginning of the next, “lapping” around the armature core.   – There are as many parallel paths as there are poles in the machine.   – At the commutator, adjacent segments are interconnected by short pitch conductors that “lap” back on themselves rather than connecting end-to-end in a series chain. In short, if you see that the commutator segments are arranged in overlapping groups with parallel connections (rather than all in series with one another) this is a clear indication of a lap winding. ───────────────────────────── Summary of Answers ───────────────────────────── 7.1.1 Answer: Assuming a star primary and delta secondary, the calculated secondary phase (and hence line) voltage is approximately 32.9 V. 7.1.2 Answer: The transformer can deliver approximately 526 A on the secondary side, given its 30 kVA rating. 7.2 Answer: Transformers operate by electromagnetic induction. A varying current in the primary produces a changing magnetic flux in the core, which induces an EMF in the secondary winding according to Faraday’s law; the voltage ratio is set by the turns ratio. 8.1 Answer: A moving copper conductor in a magnetic field experiences Lorentz forces that separate charges, thereby inducing a motional EMF proportional to the magnetic field strength, the wire’s length, and its velocity. 8.2 Answer: In a motor, a current-carrying conductor placed in a magnetic field experiences a force that produces torque, converting electrical energy into mechanical rotation. 8.3 Answers:   • 8.3.1 Hoist or lift: Series-wound DC motor (for high starting torque).   • 8.3.2 Fan: Shunt-wound DC motor (for constant speed operation).   • 8.3.3 Varying load with constant speed: Compound-wound DC motor (for good speed regulation). 8.4 Answer: A lap-wound armature is immediately recognized by its commutator connections, where each coil’s end is connected to the start of the next forming multiple parallel paths (equal in number to the poles), and the overlapping or “lapping” connections on the commutator indicate a lap winding. These are the complete answers in full detail.