EX-402 Electrical Machine - I - Jun 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aExplain the construction and working principle of a single phase transformer and derive its EMF equations.
   How to answer

   • Core, windings, construction types (core vs shell)
   • Working principle - mutual induction, alternating flux
   • Flux variation and induced e.m.f. in primary and secondary
   • Derivation of E = 4.44 f N Phi_m step by step
   • Transformation ratio and diagram
2. 7 Marks
   bA single phase 50 Hz transformer has 100 turns on the primary and 400 turns on the secondary winding. The net cross-sectional area of core is $250 \text{ cm}^2$. If the primary winding is connected to a 230 V, 50 Hz supply, determine,

   1. i)The e.m.f. induced in the secondary winding
   2. ii)The maximum value of flux density in the core.
   How to answer

   • Calculate turns ratio N2/N1
   • Secondary induced e.m.f. E2 = E1 * N2/N1
   • Use E1 = 4.44 f N1 Phi_m to find Phi_m
   • Calculate flux density Bm = Phi_m / Ai
3. 7 Marks
   aExplain the process of finding efficiency of transformer by Sumpner's test.
   How to answer

   • Circuit connection for Sumpner's test - two identical transformers back to back
   • Excitation for iron loss and short-circuit for copper loss
   • Measurement of wattmeters and procedure
   • Calculation of efficiency from losses
   • Advantage of full-load test without actual load
4. 7 Marks
   bA 40 kVA transformer has iron loss of 450 W and full-load copper loss of 850 W. If the power factor of the load is 0.8 lagging. Calculate

   1. i)Full-load efficiency
   2. ii)The kVA load at which maximum efficiency occurs and
   3. iii)The maximum efficiency.
   How to answer

   • Full-load output = kVA x pf
   • Full-load efficiency = output/(output+Pi+Pcu)
   • Condition for maximum efficiency Pi = x^2 Pcu
   • kVA at max efficiency = rated x sqrt(Pi/Pcu)
   • Calculate maximum efficiency value
5. 7 Marks
   aExplain Scott connection for 3 phase to 2 phase conversion and show that the primary neutral divides the teaser primary winding in the ratio 2:1.
   How to answer

   • Scott connection using main and teaser transformers
   • 3-phase to 2-phase phasor relationship
   • Voltage and turns relations
   • Proof that neutral divides teaser in 2:1
   • Vector diagram
6. 7 Marks
   bTwo single-phase transformers A and B rated at 600 kVA and 500 kVA respectively are operated in parallel to supply a load of 1000 kVA at 0.8 lagging power factor. The resistance and reactance of transformer A are 3% and 6.5% while that of transformer B are 1.5% and 8%. Calculate the kVA loading and the power factor at which each transformer operates.
   How to answer

   • Express %R and %X as pu impedances
   • Parallel operation load sharing formulas using admittances
   • Calculate kVA loading of transformer A and B
   • Calculate operating power factor angles
   • Check total 1000 kVA at 0.8 lagging
7. 7 Marks
   aWhat is a main differences between Squirrel Cage and Slip Ring Induction Motors?
   How to answer

   • Rotor construction: bars vs wound + slip rings
   • Starting torque, starting current differences
   • Speed control and external resistance
   • Maintenance, cost and applications
   • Summary table of differences
8. 7 Marks
   bA 150 kW 3000 V, 50 Hz, 6-pole star-connected induction motor has a star- connected slip ring rotor with a transformation ratio of 3:6 (stator/rotor). The rotor resistance is $0.1 \Omega$ per phase and its per phase leakage inductance is 3.61 mH. The stator impedance may be neglected. Find the starting current on rated voltage with short-circuited slip rings.
   How to answer

   • Refer rotor values to stator using transformation ratio
   • Synchronous speed Ns = 120f/P
   • Starting slip s=1, impedance at start
   • Starting current per phase = Vph / Z
   • Neglect stator impedance as stated
9. 7 Marks
   aExplain the No load tests and blocked rotor tests for an 3-phase induction motor.
   How to answer

   • Purpose and connections of no-load test
   • Determination of magnetizing branch and iron loss
   • Blocked rotor test at reduced voltage
   • Determination of leakage impedance and copper loss
   • Separation of parameters from test data
10. 7 Marks
    bExplain the phenomenon of cogging and crawling. Also discuss double cage and deep bar induction motor.
    How to answer

    • Definition of cogging - slot locking at start
    • Definition of crawling - stable at 1/7 speed due to harmonics
    • Causes: slot harmonics, 5th and 7th
    • Double cage construction and characteristics
    • Deep bar effect and slip-dependent resistance
11. 7 Marks
    aDraw and explain the equivalent circuit of a three-phase induction motor.
    How to answer

    • Per-phase equivalent circuit with stator, rotor and magnetizing branch
    • Symbols for R1, X1, R2/s, X2, Rc, Xm
    • Neat labeled circuit diagram
    • Power flow and slip representation
    • Explanation of each parameter
12. 7 Marks
    bExplain the double revolving field theory, equivalent circuit and its determination of single phase induction motor.
    How to answer

    • Single-phase field as two oppositely revolving fields
    • Forward and backward slip concepts
    • Equivalent circuit with forward and backward impedance
    • No-load and blocked rotor determination
    • Torque-slip from double revolving theory
13. 7 Marks
    aExplain the construction and working principle of a single phase linear induction motor.
    How to answer

    • Construction: primary and secondary, LIM layout
    • Travelling field production principle
    • Working with linear motion and slip
    • Thrust and applications
    • Diagram of linear motor
14. 7 Marks
    bA 4-pole, 250 W, 115 V, 60 Hz capacitor-start induction motor takes a full-load line current of 5.3 A while running at 1760 r.p.m. If the full load efficiency of the motor is 64%, find

    1. i)Motor slip
    2. ii)Power factor and
    3. iii)Full-load torque.
    How to answer

    • Synchronous speed Ns = 120f/P, slip = (Ns-N)/Ns
    • Input power Pin = V*I*pf, output 250W and efficiency to find pf
    • Power factor = Pin/(V*I)
    • Full-load torque T = Pout / omega_m
    • Convert rpm to rad/s
15. 14 Marks
    Write short notes on: (any Two)

    1. a)Power and distribution transformer.
    2. b)Pulse and high frequency transformers.
    3. c)How do changes in supply voltage and frequency affect the performance of an induction motor?
    4. d)Losses and efficiency of three phase induction motor.
    How to answer

    • Power vs distribution transformer: rating, design, efficiency
    • Pulse and high frequency transformer features
    • Effect of voltage and frequency variation on torque, speed, losses
    • Losses components and efficiency calculation for 3-phase IM
    • Diagrams and applications where relevant