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BT-104 · Basic Electrical & Electronics Engineering/Quick Revision Short Notes

Basic Electrical & Electronics Engineering (BT-104) - Unit 4 Short Notes

How unit 4 is examined

This unit covers DC, induction and synchronous machines; the marks sit in machine construction, the working of the 3-phase induction motor, slip numericals and machine losses.

Construction, Classification & Working Principle of DC machine, induction machine and synchronous machine

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Definition. <mark>A DC machine is a rotating machine that converts mechanical energy into DC electrical energy (generator) or DC electrical energy into mechanical energy (motor) by electromagnetic induction.</mark>

Diagram. Draw a 4-pole cross-section: yoke outside, pole core with pole shoe and field coil inside it, slotted armature with conductors, commutator and two carbon brushes on the shaft.

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Key points.

  1. The yoke is the cast-iron or steel outer frame; it carries the flux, holds the poles and protects the machine.
  2. The pole (core and shoe) is laminated and carries the field winding; the shoe spreads flux evenly over the air gap.
  3. The armature core is a laminated slotted cylinder that carries the armature winding; lamination reduces eddy-current loss.
  4. The commutator is a ring of insulated copper segments; it rectifies the armature AC to DC in a generator and reverses current for steady torque in a motor.
  5. Carbon brushes ride on the commutator and connect the rotating armature to the external circuit.
  6. Working: a generator induces emf in conductors cutting flux (Faraday); a motor's current-carrying conductor in a field feels force $F=BIl$.
  7. Induction machine: stator with 3-phase winding and a squirrel-cage or slip-ring rotor, working by an induced rotor current. Synchronous machine: 3-phase armature on the stator, DC-excited field on the rotor, running only at $N_s=120f/P$.

Formula. Generated emf:

$$E=\frac{P\Phi ZN}{60A}$$

with $A=2$ for wave and $A=P$ for lap. Motor: $T\propto\Phi I_a$, $N\propto\frac{V-I_aR_a}{\Phi}$.

Comparison.

Basis Separately excited Self-excited
Field supply Independent external DC source Own armature output
Residual magnetism Not needed Essential for voltage build-up
Types One Shunt, series, compound
Output stability Stable, wide voltage range Depends on terminal voltage
Field control Independent of load Varies with load

Torque-speed and speed control (separately excited motor). From $E_b=k\Phi\omega$ and $T=k\Phi I_a$:

$$\omega=\frac{V}{k\Phi}-\frac{R_a}{(k\Phi)^2}T$$

The line droops slightly with torque because of the armature resistance drop. Speed is controlled by armature voltage (below rated speed) or field flux (above rated speed).

Example. 8-pole, wave ($A=2$), $Z=600$, $\Phi=0.08$ Wb, $N=215$ rpm. $E=\frac{8\times0.08\times600\times215}{60\times2}=$ 688 V. For 500 V: $N=\frac{60\times2\times500}{8\times0.08\times600}=$ 156.25 rpm (if flux is 0.05 Wb as in the Hindi text, 250 rpm).

Answer frame. Open with the definition and draw the labelled cross-section; describe each part with its function (points 1-5); close with generator and motor action. For the comparison, draw both circuits and tabulate. For the motor, write the speed and torque equations, sketch the drooping line, and end with the two control methods.

Asked: [7 marks] (Dec 2024, Jun 2025) Describe D.C. machine with suitable sketches in viewing of main parts and construction details. Asked: [7 marks] (Jun 2022) Explain the torque-speed characteristic and speed control of separately excited DC motor. Asked: [7 marks] (Nov 2022) Explain the construction and working principle of three-phase induction motor with suitable diagram. Asked: [7 marks] (Nov 2022) What is the difference between a separately excited and a self-excited generator? Asked: [7 marks] (Nov 2022) An 8-pole DC machine has a wave winding containing 600 conductors. Calculate the generated e.m.f when the flux per pole is 0.08 Wb and speed is 215 rpm. At what speed should the armature be driven to generate 500V.

Working principle of 3-Phase induction motor

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">High weight</span>

Definition. <mark>A 3-phase induction motor runs on the rotating magnetic field set up by its stator; the rotor receives its current by induction, never by a supply connection.</mark>

Diagram. Draw stator with 3-phase winding, air gap and rotor inside.

<figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u4-02" viewBox="0 0 338 80" width="338" height="80" role="img" aria-label="S = stator 3-phase winding, R = rotor conductors, T = rotor turns in the direction of the field"><style>#dsfig-u4-02 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u4-02 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u4-02 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u4-02 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u4-02 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u4-02 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u4-02 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u4-02 .t{fill:#16181D;font-weight:500}#dsfig-u4-02 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u4-02 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u4-02 .dot{fill:#16181D}#dsfig-u4-02 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u4-02 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u4-02 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u4-02 .ah{fill:#454C5A}#dsfig-u4-02 .ah.hi{fill:#2340B8}#dsfig-u4-02 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u4-02 .wl .t{font-size:12px;font-weight:700}#dsfig-u4-02 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u4-02 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u4-02 .e{stroke:#B1B7C3}html.dark #dsfig-u4-02 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u4-02 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u4-02 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u4-02 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u4-02 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u4-02 .t{fill:#E6E8ED}html.dark #dsfig-u4-02 .t.inv{fill:#0F1115}html.dark #dsfig-u4-02 .kd{stroke:#E6E8ED}html.dark #dsfig-u4-02 .dot{fill:#E6E8ED}html.dark #dsfig-u4-02 .ann{fill:#8FA3FF}html.dark #dsfig-u4-02 .lbl{fill:#858D9C}html.dark #dsfig-u4-02 .ptr{fill:#8FA3FF}html.dark #dsfig-u4-02 .ah{fill:#B1B7C3}html.dark #dsfig-u4-02 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u4-02 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u4-02 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u4-02 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah11" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh11" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M59,40 L148,40" marker-end="url(#ah11)"/><path class="e" d="M188,40 L277,40" marker-end="url(#ah11)"/><g class="wl"><rect x="87.7" y="31" width="33.6" height="18" rx="9"/><text class="t" x="104.5" y="40" dy=".35em" text-anchor="middle">RMF</text></g><g class="wl"><rect x="206.4" y="31" width="54.3" height="18" rx="9"/><text class="t" x="233.5" y="40" dy=".35em" text-anchor="middle">torque</text></g><circle class="n" cx="40" cy="40" r="18"/><text class="t" x="40" y="40" dy=".35em" text-anchor="middle">S</text><circle class="n" cx="169" cy="40" r="18"/><text class="t" x="169" y="40" dy=".35em" text-anchor="middle">R</text><circle class="n" cx="298" cy="40" r="18"/><text class="t" x="298" y="40" dy=".35em" text-anchor="middle">T</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">S = stator 3-phase winding, R = rotor conductors, T = rotor turns in the direction of the field</figcaption></figure>

Key points.

  1. The stator has a laminated silicon-steel core with a 3-phase distributed winding placed in slots.
  2. The squirrel-cage rotor has bars short-circuited by end rings; the slip-ring (wound) rotor has a 3-phase winding brought out through slip rings for external resistance.
  3. Three currents 120 degrees apart produce a rotating field of constant magnitude $1.5\Phi_m$ at $N_s=\frac{120f}{P}$.
  4. The field cuts the stationary rotor conductors and induces an emf in them by Faraday's law.
  5. The rotor is short-circuited, so the emf drives rotor current, and the current in the field gives a force $F=BIl$ and torque $T\propto\Phi I_r\cos\phi_2$.
  6. By Lenz's law the rotor opposes the relative motion between field and conductors, so it turns in the direction of the field.
  7. The rotor cannot reach $N_s$: at $N=N_s$ there is no relative speed, so no emf, no current and no torque. It runs slightly slower, and the difference is the slip.

Answer frame. Open with the definition; draw stator and rotor with labels; give points 1-2 for construction, then 3-6 in order; close with point 7 and the slip formula $s=\frac{N_s-N}{N_s}$. For "why not synchronous speed", quote point 7 and add that the torque-slip curve passes through zero at $s=0$.

Asked: [7 marks] (Jun 2022, Jun 2025) Explain the principle of operation of 3-phase induction motor. Asked: [7 marks] (Jun 2023) Explain the construction and working principle of three phase induction motor with suitable diagram. Asked: [7 marks] (Dec 2024) Discuss the construction and working principle of the three phase induction motor. Draw the torque slip characteristic of the above. Why this motor cannot operate on synchronous speed?

Concept of slip in 3-Phase induction motor

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Medium weight</span>

Definition. ==Slip is the fractional difference between synchronous speed and rotor speed: $s=\frac{N_s-N}{N_s}$.==

Key points.

  1. Slip is zero at synchronism and 1 at standstill; a healthy motor runs at 2-5% slip on full load.
  2. Rotor speed is $N=N_s(1-s)$, and slip speed is $N_s-N$.
  3. Rotor current frequency is $f_r=sf$; it equals $f$ at start and falls to 1-3 Hz at full load.
  4. Rotor emf at slip $s$ is $E_r=sE_2$, where $E_2$ is the standstill value.
  5. Load increases slip, and the larger $E_r$ raises rotor current and torque until they balance the load.

Example 1. 6 pole, 50 Hz: $N_s=\frac{120\times50}{6}=$ 1000 rpm; $N_0=1000(1-0.01)=$ 990 rpm; $N_{fl}=1000(1-0.03)=$ 970 rpm; $f_r=0.03\times50=$ 1.5 Hz.

Example 2. 50 Hz, 1440 rpm: nearest $N_s$ above is 1500, so $P=\frac{120\times50}{1500}=$ 4 poles; $s=\frac{1500-1440}{1500}=$ 0.04; slip speed 60 rpm. Rotor speed is 1440 rpm w.r.t. stator, 60 rpm w.r.t. the rotating mmf (backward), and 0 w.r.t. its own structure. Taking 440 V as the standstill stator phase emf, $E_2=440\times0.5=220$ V and $E_r=0.04\times220=$ 8.8 V.

Answer frame. Write the given data, then $N_s$, $N$, $s$ and $f_r$ in order, one formula each, and box every result.

Asked: [7 marks] (Jun 2023, Dec 2024) A three phase, 6 pole, 50 Hz induction motor has a slip of 1% at no load and 3% at full load. Find synchronous speed, no load speed, full load speed and frequency of rotor current at full load. Asked: [7 marks] (Jun 2023, Dec 2024) A three phase 440 volt, 50 hp, 50 Hz induction motor delivers rated output power at 1440 rpm. Find the number of poles, synchronous speed, slip, slip rpm, rotor speed w.r.t. rotor structure, stator and stator rotating mmf, and rotor emf if stator to rotor turns ratio is 1:0.5 (winding factor unity).

Torque-slip characteristics of 3-Phase induction motor

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Low weight</span>

Definition. <mark>The torque-slip characteristic plots motor torque against slip, using $T\propto\frac{sE_2^2R_2}{R_2^2+(sX_2)^2}$.</mark>

Key points.

  1. At small slip $sX_2\ll R_2$, so $T\propto s$; the curve is nearly a straight line and the motor works stably here.
  2. At large slip $sX_2\gg R_2$, so $T\propto\frac1s$; the curve falls as slip increases.
  3. Maximum (pull-out) torque occurs at $s_m=\frac{R_2}{X_2}$; starting torque is the value at $s=1$.
  4. The full curve has three regions:
Region Slip Behaviour
Generating $s<0$ Rotor above $N_s$; power returned to the supply
Motoring $0<s<1$ Torque rises to maximum, then falls to starting torque
Braking (plugging) $s>1$ Rotor turns against the field, torque acts as a brake
  1. Adding rotor resistance moves $s_m$ towards 1 and raises the starting torque without changing the maximum torque.

Asked: [7 marks] (Dec 2023) Draw and explain the complete Torque-slip characteristics of 3 phase induction motor.

Types of losses occurring in electrical machines

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Definition. ==Losses are the part of input power that is not delivered as output; they appear as heat and set the efficiency $\eta=\frac{\text{output}}{\text{input}}$.==

Diagram.

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Key points.

  1. Copper loss $I^2R$ occurs in the armature, field and stator or rotor windings; it varies with the square of the load current.
  2. Hysteresis loss is $P_h=k_hB_{max}^{1.6}fv$; it comes from repeated magnetic reversal of the core and is cut by silicon steel.
  3. Eddy-current loss is $P_e=k_eB_{max}^2f^2t^2v$; it comes from currents induced in the core and is cut by thin laminations.
  4. Hysteresis and eddy loss together are the iron (core) loss, which is constant at constant voltage and frequency.
  5. Mechanical loss is bearing and brush friction plus air windage; it is constant at constant speed.
  6. Stray load loss and brush contact loss are small extra losses that rise with load.
  7. Maximum efficiency occurs when variable loss equals constant loss.

Example. Core = mechanical = 100 W, stator copper 150 W, output 2000 W, $s=0.04$. $P_{mech}=2000+100=2100$ W; $P_g=\frac{2100}{0.96}=2187.5$ W (rotor copper loss $=87.5$ W); $P_{in}=2187.5+150+100=2437.5$ W. $\eta=\frac{2000}{2437.5}\times100=$ 82.05%.

Answer frame. Open with the definition; draw the classification tree; explain each class in the order copper, iron, mechanical, stray; close with the efficiency formula. For the numerical, chain $P_{mech}$, $P_g$, $P_{in}$, $\eta$.

Asked: [14 marks] (Jun 2022, Jun 2023) Write short notes on (any two): a) Voltage Regulation b) Types of losses occurring in electrical machines c) Logic Gates d) Half and full adder circuits Asked: [7 marks] (Dec 2023) The core loss in a 3 phase induction motor is 100 W and equals the mechanical loss, stator copper loss is 150 W. When developing 2000 W as the shaft power, what is the efficiency? Assume slip 4%.

Applications of DC machine, induction machine and synchronous machine

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Low weight</span>

Definition. <mark>Each machine type is chosen by its speed-torque behaviour.</mark>

Key points.

  1. DC shunt motors run at nearly constant speed, so they drive lathes, centrifugal pumps, fans and conveyors.
  2. DC series motors give very high starting torque, so they suit electric traction, cranes, hoists and elevators.
  3. DC compound motors combine both, so they suit rolling mills, heavy presses and elevators.
  4. DC generators serve battery charging, electroplating and as exciters for alternators.
  5. Induction motors drive pumps, fans, compressors and workshop machines; synchronous machines are the alternators of power stations and, as synchronous motors, correct power factor.

Asked: [7 marks] (Nov 2022) Explain in detail the Applications of DC Machines.

Last-minute revision

  • $N_s=\frac{120f}{P}$; $s=\frac{N_s-N}{N_s}$; $N=N_s(1-s)$; $f_r=sf$; $E_r=sE_2$.
  • DC emf: $E=\frac{P\Phi ZN}{60A}$; $A=2$ wave, $A=P$ lap.
  • Rotating field magnitude is $1.5\Phi_m$ at $N_s$.
  • Motor speed $N\propto\frac{V-I_aR_a}{\Phi}$; torque $T\propto\Phi I_a$.
  • Speed control: armature voltage below rated speed, field flux above.
  • Maximum torque at $s_m=R_2/X_2$; braking $s>1$, generating $s<0$.
  • $P_g=\frac{P_{mech}}{1-s}$; rotor copper loss $=sP_g$.
  • Iron loss = hysteresis + eddy; mechanical loss = friction + windage.
  • 8-pole wave, 600 conductors: 688 V; 1440 rpm on 50 Hz is 4 poles, 4% slip.
  • Answers: 1000/990/970 rpm and 1.5 Hz; efficiency 82.05%.

Memory hooks

  • Yoke, Poles, Armature, Commutator, Brushes: "YPACB".
  • Slip zero means torque zero: the rotor never catches the field.
  • Shunt is steady (fans), series is strong (cranes).
  • Losses: Copper varies with load, Iron and Mechanical stay constant.
  • Torque-slip: rises like $s$, falls like $1/s$.

Coverage checklist

  • Construction, Classification & Working Principle of DC machine, induction machine and synchronous machine: DC parts, torque-speed, generator comparison, EMF numerical, 3-phase induction motor construction.
  • Working principle of 3-Phase induction motor: principle of operation, construction and working, why not synchronous speed.
  • Concept of slip in 3- Phase induction motor: both slip numericals.
  • Explanation of Torque-slip characteristics of 3-Phase induction motor: complete torque-slip curve.
  • Types of losses occurring in electrical machines: short note on losses, efficiency numerical.
  • Applications of DC machine, induction machine and synchronous machine: applications of DC machines.
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