HSC Exam Practice

Sample response. Slip is the percentage by which the rotor speed falls below the synchronous speed of the stator field: % slip = (n_s − n_r) / n_s × 100, where n_s is synchronous speed and n_r is rotor speed. Slip cannot be zero during normal operation because induction only occurs when there is relative motion between the stator field and the rotor. If the rotor reached synchronous speed, there would be no relative motion, no changing flux in the rotor bars, no induced emf (Faraday’s Law), no induced currents, and therefore no torque to keep the rotor spinning.

Marking notes. 1 mark for a correct definition or formula for slip; 1 mark for stating that slip cannot be zero; 1 mark for explaining the reason using Faraday’s Law (no flux change = no induction = no torque) or equivalent.

Sample response. Stage 1: Three-phase AC in the stator windings creates a rotating magnetic field (no induction law — this is the electrical input). Stage 2: The rotating field sweeps past the rotor bars; by Faraday’s Law, the changing flux through each bar induces an emf and drives a current through the squirrel cage. Stage 3: By Lenz’s Law, the induced rotor currents create a magnetic field opposing the relative motion between rotor and stator field; this opposition produces the force (torque) that drags the rotor around in the direction of the stator field.

Marking notes. 1 mark per stage correctly described with the relevant law named where applicable. Accept responses that combine stages 2 and 3 if both laws are correctly applied.

Sample response. (a) n_s = 120f / p = 120 × 50 / 6 = 1000 RPM. (b) Slip speed = 1000 − 960 = 40 RPM. (c) % slip = 40 / 1000 × 100 = 4.0%.

Marking notes. 1 mark for correct synchronous speed (1000 RPM); 1 mark for correct slip speed (40 RPM); 1 mark for correct percentage slip (4.0%). Penalise if formula not shown but allow error carried forward.

Sample response. In an AC induction motor, the rotor is a squirrel cage of conducting bars with no external electrical connection. It rotates because currents are induced in it by the changing flux of the stator field; the rotor converts electrical energy (supplied to the stator) into mechanical (kinetic) energy at the shaft. In a power station generator, the rotor is an electromagnet excited by a DC current. A turbine spins the rotor inside the stationary stator windings; as the rotor turns, the changing magnetic flux through the stator coils induces a large alternating emf, converting mechanical energy from the turbine into electrical energy for the grid.

Marking notes. 1 mark for correct description of the motor rotor (squirrel cage, no electrical connection, driven by induction); 1 mark for correct energy conversion in the motor (electrical → mechanical); 1 mark for correct description of the generator rotor (electromagnet, DC excited, spun by turbine); 1 mark for correct energy conversion in the generator (mechanical → electrical).

Sample response. AC is used because it can be stepped up to high voltages using transformers for long-distance transmission, greatly reducing resistive (I²R) power losses in transmission lines; DC cannot be efficiently transformed with a simple transformer. The use of 50 Hz AC means that power station generators must rotate at a speed that produces exactly 50 Hz: for a 2-pole generator, this is 3000 RPM, while a 4-pole generator must run at 1500 RPM. Generator design must therefore match turbine speed to pole number to maintain the correct output frequency.

Marking notes. 1 mark for correctly stating that AC is used because transformers step voltage up/down (reduces transmission losses); 1 mark for linking the choice of 50 Hz to generator rotation speed via n = 120f/p; 1 mark for a specific consequence for generator design (pole number or rotational speed specified).

Sample response. Advantage 1: No brushes or commutator. In a DC motor, carbon brushes press against a rotating commutator to maintain electrical contact; these wear away over time and require frequent replacement, causing unplanned downtime. The squirrel cage induction motor has no brushes or commutator — the rotor current is induced, not conducted through a contact — so there is no brush wear, much lower maintenance, and greater suitability for continuous 16-hour operation. Advantage 2: More robust and safer in industrial environments. Because the rotor has no external wiring or contacts, it is inherently sealed and can operate in dusty, wet, or explosive-atmosphere conditions where electrical sparking from brushes would create fire or explosion risks. The simpler rugged construction also withstands vibration better.

Marking notes. 1 mark for stating advantage 1 (no brushes/commutator) with reference to reduced wear; 1 mark for explaining the physical basis (rotor current induced rather than conducted through a contact); 1 mark for stating advantage 2 (any valid second advantage: robust construction, sealed design, simpler, more efficient, lower maintenance cost — accept any well-reasoned second advantage); 1 mark for explaining the physical basis of the second advantage.

Sample response (a). In the normal operating region (0–20 N m), rotor speed decreases approximately linearly as shaft torque increases: from near-synchronous speed (1498 RPM) at no load to about 1440 RPM at rated load. The relationship arises from slip: as load increases, the rotor slows, increasing the slip and therefore the relative motion between stator field and rotor. Greater slip increases the rate of flux change (Faraday’s Law), inducing larger rotor currents and producing greater torque to balance the load. [1 mark — describes nearly linear speed decrease; 1 mark — links to increasing slip; 1 mark — explains mechanism via Faraday and induced current]

Sample response (b). Synchronous speed n_s = 120 × 50 / 4 = 1500 RPM. Slip speed = 1500 − 1440 = 60 RPM. % slip = (60 / 1500) × 100 = 4.0%. [1 mark for correct n_s and slip speed; 1 mark for correct % slip]

Sample response (c). As load (torque demand) increases, the rotor encounters greater mechanical resistance and slows down. The slower rotor falls further behind the stator field, increasing slip. Greater slip means greater relative motion between stator field and rotor bars, which by Faraday’s Law increases the rate of flux change, inducing larger rotor currents and hence greater electromagnetic torque. The rotor settles at a new, lower speed where the increased electromagnetic torque matches the increased load. [1 mark for explaining slip increases with load; 1 mark for linking increased slip to larger induced rotor current and torque via Faraday’s Law]

Marking notes. Part (a): 3 marks as annotated. Part (b): 2 marks. Part (c): 2 marks.

Sample response. Electromagnetic induction, described by Faraday’s Law (emf = −dΦ/dt), underpins both the AC induction motor and the large-scale generator, yet the energy conversion proceeds in opposite directions in each device. In an induction motor, the stator is fed three-phase AC, which creates a rotating magnetic field. This rotating field passes through the conducting bars of the squirrel cage rotor, inducing an emf (Faraday’s Law) and driving currents around the squirrel cage. By Lenz’s Law, these induced currents generate a force opposing the relative motion between the field and the rotor bars, pulling the rotor in the direction of the rotating field and producing mechanical torque. The energy conversion is from electrical (supplied to the stator) to mechanical (shaft rotation). Slip is essential in the motor because induction requires relative motion between the field and the rotor; if the rotor reached synchronous speed, the rate of flux change would be zero, no emf would be induced, and no torque produced. Typical slip is 2–5%, representing a small but irreducible efficiency loss. In a power station generator — for example, the Eraring Power Station on Lake Macquarie, the largest thermal generator in Australia — the process is reversed. A steam turbine spins the rotor (an DC-excited electromagnet) at synchronous speed (typically 3000 RPM for a 2-pole generator producing 50 Hz). As the rotor turns, the magnetic flux through the stationary stator windings changes continuously; by Faraday’s Law, a large alternating emf is induced in the stator coils, which drives current to the national grid after stepping up through transformers. Here there is no slip — the generator must run at exactly synchronous speed because any deviation changes the output frequency, destabilising the grid. Lenz’s Law manifests in the generator as the back-torque: the induced stator current creates a magnetic field opposing the rotor rotation, meaning the turbine must continuously supply mechanical energy to overcome this resistance and maintain constant speed. The significance of these technologies for the Australian National Electricity Market (NEM) is profound: virtually all grid electricity is generated by synchronous generators, and approximately 70% of Australia’s industrial electricity consumption is by AC induction motors. Their reliability, efficiency, and lack of commutators makes them the backbone of mining, water treatment, and manufacturing. Understanding both devices and the central role of electromagnetic induction is therefore not merely theoretical but fundamental to the operation of the modern Australian economy.

Marking criteria (7 marks). 1 = Faraday’s Law correctly applied to the motor (rotating field induces emf in rotor bars). 1 = Lenz’s Law correctly applied to the motor (induced currents produce torque opposing relative motion). 1 = energy conversion in motor correctly stated (electrical → mechanical) with reference to the role of slip. 1 = Faraday’s Law correctly applied to the generator (spinning rotor flux induces emf in stator). 1 = explains why slip is necessary in the motor but not the generator, with correct reasoning (motor needs relative motion for induction; generator runs synchronously for correct frequency output). 1 = names and uses a specific Australian generator or industrial example correctly (Eraring, Snowy Hydro, Liddell — any valid example). 1 = reaches an explicit evaluative judgement about the significance of electromagnetic induction to both devices and/or the Australian energy system.