EEE Theoretical Questions from PYQ

eee-1109 EEE-1109 Basic Electrical Engineering

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Key Definitions

Reluctance (ℜ)
Reluctance is the opposition offered by a magnetic circuit to the establishment of magnetic flux.

$\mathcal{R}=\frac{l}{\mu A}$

Where ( l ) = length of magnetic path, ( A ) = cross-sectional area, $(\mu )$ = permeability of material.

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Permeability (μ)
Permeability is the ability of a material to allow magnetic flux to pass through it.

$\mu ={\mu }_0{\mu }_r$

Where ( \mu_0 ) is permeability of free space and ( \mu_r ) is relative permeability.

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Permeance (P)
Permeance is the ease with which a magnetic flux is established in a material.

$P=\frac{1}{\mathcal{R}}=\frac{\mu A}{l}$

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Magnetomotive Force (MMF)
MMF is the magnetic driving force that sets up magnetic flux in a circuit.

$\text{MMF}=NI$

Where ( N ) = number of turns, ( I ) = current.

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Flux Density (B)
Flux density is the magnetic flux per unit area.

$B=\frac{\Phi }{A}$

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Difference Between Electrical and Magnetic Circuit

Electrical Circuit	Magnetic Circuit
Current (I) flows.	Flux (Φ) flows.
Opposed by resistance (R).	Opposed by reluctance (ℜ).
Driving force is voltage (V).	Driving force is MMF (NI).
Power is consumed (I²R loss).	No actual power loss in ideal case.
Conductance depends on material conductivity.	Permeance depends on material permeability.

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Ampere’s Law

Statement:
The line integral of magnetic field intensity ( H ) around any closed path equals the total current enclosed by the path.

$\oint H\cdot dl=I_{\text{enclosed}}$ $\therefore H=\frac{I}{2\pi S}$

Explanation:
This law relates magnetic field around a conductor to the current producing it.

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Biot–Savart Law

Statement:
The magnetic field ( dB ) produced at a point by a small current element ( Idl ) is directly proportional to the current, the element length, and the sine of the angle between them, and inversely proportional to the square of the distance between them.

$dB=\frac{{\mu }_0}{4\pi }\frac{I,dl\sin \theta }{r^2}$

$\boxed{B=\frac{\mu I}{2\pi r}}\text{(weber per sq. meter)}$

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Derivation: Magnetic Flux Density at Distance ( r ) from Long Straight Conductor

Using Ampere’s Law,

$\oint H,dl=I$

For a circular path of radius ( r ):

$H(2\pi r)=I\Rightarrow H=\frac{I}{2\pi r}$

Since $(B=\mu H)$,

$B=\mu \frac{I}{2\pi r}$

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Applications of Magnetic Circuits

• Transformers

• Electric motors

• Generators

• Electromagnets

• Relays and magnetic sensors

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Hysteresis Loss

When the magnetic material in a core is magnetized and demagnetized repeatedly (as in AC operation), the flux lags behind the magnetizing force due to molecular friction inside the material. This lag causes energy loss in the form of heat, known as hysteresis loss.

$P_h=\eta f{B}_{\max }^{n}V$

Where:
$(\eta )$ = Steinmetz constant (material dependent)
$(f)$ = frequency
$(B_{\max })$ = maximum flux density
$(n\approx 1.6)to(2)$ $(V)$ = volume of the core

Minimization:

• Use soft magnetic materials with narrow hysteresis loops, e.g., silicon steel, ferrites.

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Eddy Current Loss

When magnetic flux through a metallic core changes, small circulating currents are induced in the body of the core. These currents (called eddy currents) flow in closed loops inside the material and cause heat loss.

$P_e=K_e{B}_{\max }^2{f}^2{t}^{2}V$

Where:
$(t)$ = thickness of each lamination

Minimization:

• Use laminated cores instead of solid iron

• Increase electrical resistivity of core (add silicon)

• Use ferrite core for high-frequency applications

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Hysteresis Loop

A hysteresis loop is the curve obtained by plotting magnetic flux density (B) against magnetizing force (H) during a cycle of magnetization.

Key Points:

• Retentivity: The value of ( B ) when ( H = 0 ). Indicates how much flux remains after magnetizing force is removed.

• Coercive Force: The value of ( H ) needed to make ( B = 0 ). Indicates effort to demagnetize.

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Difference Between Soft and Hard Magnetic Materials Using Hysteresis Loop

Property	Soft Magnetic Material	Hard Magnetic Material
Hysteresis Loop Area	Small (low hysteresis loss)	Large (high hysteresis loss)
Coercive Force	Low	High
Retentivity	Low to moderate	High
Ease of Magnetization / Demagnetization	Very easy	Difficult
Typical Use	Electromagnets, transformer cores, motors	Permanent magnets, speakers, magnetic locks

Graph Description (write if diagram not allowed):
Soft materials have a thin, narrow hysteresis loop.
Hard materials have a wide, broad hysteresis loop.

Summary Paragraph

During AC operation, magnetic materials are subjected to repeated magnetization cycles. Due to molecular friction, energy is lost inside the material, known as hysteresis loss. This loss is proportional to the area enclosed by the B-H loop and is minimized by using soft core materials like silicon steel. Also, time-varying flux produces eddy currents in the core, which circulate and cause heat loss. These losses are minimized by using laminated cores with increased electrical resistivity. A hysteresis loop (B-H curve) represents the relationship between magnetic flux density and magnetizing force, showing retentivity and coercive force. Soft magnetic materials have a narrow loop with low coercive force, while hard materials have a wide loop and are used for permanent magnet applications.

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