Question 1(a) [3 marks]

Define accuracy and precision.

Answer:

Accuracy: Closeness of a measured value to the true value
Precision: Consistency or repeatability of measurement values

Mnemonic: "Accuracy Aims at Truth, Precision Produces Repeatability"

Question 1(b) [4 marks]

Derive SI unit of work and Velocity using fundamental physical units.

Answer:

Table: Derivation of Work and Velocity Units

Physical Quantity	Formula	SI Unit Derivation	SI Unit
Work (W)	W = F × d	W = [Force] × [Distance] = [kg·m/s²] × [m] = [kg·m²/s²]	Joule (J)
Velocity (v)	v = d/t	v = [Distance]/[Time] = [m]/[s]	m/s

Work: When a force (kg·m/s²) acts through a distance (m), we get kg·m²/s² = Joule
Velocity: When an object covers distance (m) in time (s), we get m/s

Mnemonic: "Work Forces Distance, Velocity Distances Time"

Question 1(c) [7 marks]

What is Least Count of instrument. State equation of Least count of Vernier calipers. Explain measurement by vernier calipers with neat and clean diagram.

Answer:

Least Count: Smallest measurement that can be directly measured using a measuring instrument.

Equation for Least Count of Vernier Caliper: Least Count = 1 Main Scale Division - 1 Vernier Scale Division or Least Count = Value of 1 MSD / Number of VSD

Diagram: Vernier Caliper

      ┌────────┐
      │        │
 ┌────┘    ┌───┘
 │         │
 │   ┌─────┘
 │   │
─┼───┼───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬
 0   1   2   3   4   5   6   7   8   9   10
     │   │   │   │   │   │   │   │   │
     └───┴───┴───┴───┴───┴───┴───┴───┴───┘ 
      0   5  10  15  20  25  30  35  40  45
      Vernier Scale

Measurement Process:

Step 1: Close the jaws of caliper around the object
Step 2: Note the main scale reading just before the zero of vernier scale
Step 3: Find which vernier division exactly coincides with a main scale division
Step 4: Add the vernier reading to the main scale reading: Total = MSR + (VC × LC)
Main Scale Reading (MSR): Value on main scale just before vernier zero
Vernier Coincidence (VC): Division number where vernier line aligns with main scale line
Least Count (LC): Usually 0.02 mm or 0.001 inch

Mnemonic: "Main plus Matched makes Measurement"

Question 1(c) OR [7 marks]

What is Least Count of instrument. State equation of Least count of micrometer screw. Explain the positive and negative error in micrometer screw with neat and clean diagram.

Answer:

Least Count: Smallest measurement that can be directly measured using a measuring instrument.

Equation for Least Count of Micrometer Screw: Least Count = Pitch of screw / Number of divisions on circular scale

Diagram: Micrometer Screw Gauge

     ┌─────────────────┐
     │                 │
     │    ┌───────┐    │
     │    │       │    │
     └────┤       ├────┘
          │       │
          └───────┘
          
    0  5  10 15 20 25
    ────────────────────
       │
       V
   ┌───────┐
   │0 5    │  ← Circular Scale
   └───────┘

Positive Error: When zero of circular scale is above the reference line. The measured reading will be more than the actual value.

Negative Error: When zero of circular scale is below the reference line. The measured reading will be less than the actual value.

Error Correction:

For positive error: Actual Reading = Observed Reading - Zero Error
For negative error: Actual Reading = Observed Reading + Zero Error

Mnemonic: "Positive Produces Plus, Negative Needs Addition"

Question 2(a) [3 marks]

Write characteristics of electric lines of force.

Answer:

Table: Characteristics of Electric Field Lines

Characteristic	Description
Direction	Always from positive to negative charge
Shape	Straight lines for uniform fields, curved for non-uniform fields
Density	Proportional to field strength
Path	Never intersect each other
Nature	Start from positive and end at negative charges

Mnemonic: "Direction, Density, Never Cross, Start-End"

Question 2(b) [4 marks]

Calculate the equivalent capacitance for both series and parallel connection of capacitors having capacitance of values 9 μF, 12 μF & 15 μF.

Answer:

For Series Connection: 1/Ceq = 1/C₁ + 1/C₂ + 1/C₃ 1/Ceq = 1/9 + 1/12 + 1/15 1/Ceq = 5/36 + 3/36 + 2.4/36 = 10.4/36 Ceq = 36/10.4 = 3.46 μF

For Parallel Connection: Ceq = C₁ + C₂ + C₃ Ceq = 9 + 12 + 15 = 36 μF

Mnemonic: "Series Sums Reciprocals, Parallel Puts Together"

Question 2(c) [7 marks]

Explain coulombs inverse square law and derive its equation. Calculate coulomb force between two electrons separated by 10 meter. (e=1.66 x 10⁻¹⁹ C, K= 9 x 10⁹ Nm² C⁻²)

Answer:

Coulomb's Law: The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Equation Derivation: F ∝ q₁q₂ F ∝ 1/r² Combining: F ∝ q₁q₂/r² With constant: F = k(q₁q₂/r²)

Where k = 1/(4πε₀) = 9 × 10⁹ Nm²/C²

Diagram: Coulomb's Law

     q₁        q₂
     ●─────────●
     ←────r────→
     F₁²→   ←F₂₁

Calculation: F = k(q₁q₂/r²) F = 9 × 10⁹ × [(1.66 × 10⁻¹⁹) × (1.66 × 10⁻¹⁹)] / (10)² F = 9 × 10⁹ × 2.76 × 10⁻³⁸ / 100 F = 9 × 2.76 × 10⁻³⁸⁻² × 10⁹ F = 2.48 × 10⁻³¹ N

Mnemonic: "Charges Multiply, Distance Squares, Force Declines"

Question 2(a) OR [3 marks]

Explain electric field and and derive its unit.

Answer:

Electric Field: The region around a charge where another charge experiences a force.

Definition: Electric field at a point is the force experienced by a unit positive charge placed at that point.

E = F/q

Unit Derivation: E = F/q = [N]/[C] = [kg·m/s²]/[A·s] = [kg·m/(A·s³)] SI unit: N/C or V/m

Mnemonic: "Electric field Equals Force per Charge"

Question 2(b) OR [4 marks]

Explain electric flux with neat figure and derive its unit.

Answer:

Electric Flux: Measure of the electric field passing through a given area.

Equation: ϕₑ = E·A·cosθ

Where:

E is the electric field
A is the area
θ is the angle between E and the normal to the area

Diagram: Electric Flux

       ↑ n (normal)
       │
       │  θ
       │/
───────┼─────→ E (electric field)
       │
       │
    Surface Area A

Unit Derivation: ϕₑ = E·A·cosθ = [N/C]·[m²]·[dimensionless] = [N·m²/C] Since 1 N/C = 1 V/m, flux unit = V·m = N·m²/C

SI unit: N·m²/C or V·m

Mnemonic: "Flux Flows through Fields and Areas"

Question 2(c) OR [7 marks]

Define capacitor and derive its unit. Give the formula of parallel plate capacitor and explain each term. Calculate the capacitance of a parallel plate capacitor having 20 cm x 20 cm square plates separated by a distance of 1.0 mm.

Answer:

Capacitor: A device that stores electric charge.

Definition: Capacitance is the ratio of charge stored to the potential difference applied. C = Q/V

Unit Derivation: C = Q/V = [C]/[V] = [A·s]/[J/C] = [A·s]/[N·m/C] = [A²·s⁴/(kg·m²)] = Farad (F)

Parallel Plate Capacitor Formula: C = ε₀εᵣA/d

Where:

C is the capacitance
ε₀ is the permittivity of free space (8.85 × 10⁻¹² F/m)
εᵣ is the relative permittivity of dielectric
A is the area of overlap of plates
d is the distance between plates

Diagram: Parallel Plate Capacitor

    ┌───────────────┐ ┐
    │ + + + + + + + │ │
    └───────────────┘ │ d
    ┌───────────────┐ │
    │ - - - - - - - │ │
    └───────────────┘ ┘
          Area A

Calculation: A = 20 cm × 20 cm = 0.2 m × 0.2 m = 0.04 m² d = 1.0 mm = 0.001 m εᵣ = 1 (air) ε₀ = 8.85 × 10⁻¹² F/m

C = ε₀εᵣA/d = 8.85 × 10⁻¹² × 1 × 0.04/0.001 = 354 × 10⁻¹² F = 354 pF

Mnemonic: "Capacitance Collects Charge between Closer Plates"

Question 3(a) [3 marks]

Explain heat conduction in solid with example.

Answer:

Heat Conduction: Transfer of heat through a solid material without the movement of the material itself.

Process: Heat energy transfers from high temperature region to low temperature region through molecular vibrations.

Diagram: Heat Conduction

   Hot                Cold
    ↓                  ↓
┌────────────────────────┐
│ >>>>>>>>>>>>>>>>>>>>>>> │
└────────────────────────┘
     Heat flow →

Example: Metal spoon in hot tea gets heated up at the handle end through conduction.

Mnemonic: "Hot Energizes, Atoms Transfer, Conducts Outward"

Question 3(b) [4 marks]

A person has fever 102. What is the temperature scale here? Convert the temperature in remaining two scales.

Answer:

Temperature Scale: 102°F (Fahrenheit)

Conversion Formulas:

°C = (°F - 32) × 5/9
K = °C + 273.15

Calculation: °C = (102 - 32) × 5/9 = 70 × 5/9 = 38.89°C K = 38.89 + 273.15 = 312.04 K

Table: Temperature Conversion

Fahrenheit	Celsius	Kelvin
102°F	38.89°C	312.04 K

Mnemonic: "Fahrenheit First, Convert Celsius, Kelvin Comes last"

Question 3(c) [7 marks]

Explain the principle of platinum resistance thermometer and list out its uses.

Answer:

Principle: The electrical resistance of platinum changes predictably and consistently with temperature, allowing for precise temperature measurement.

Working: Based on the relationship R = R₀[1 + α(T - T₀)], where R is resistance at temperature T, R₀ is resistance at reference temperature T₀, and α is temperature coefficient of resistance.

Diagram: Platinum Resistance Thermometer

    ┌───────────────┐
    │   Indicator   │
    └───┬───────┬───┘
        │       │
        │       │
    ┌───┴───────┴───┐
    │   Wheatstone   │
    │     Bridge     │
    └───┬───────┬───┘
        │       │
        │       │
    ┌───┴───────┴───┐
    │   Platinum    │
    │   Resistance  │
    │     Coil      │
    └───────────────┘

Uses:

Industrial process: Temperature monitoring in manufacturing
Scientific research: Laboratory measurements requiring high precision
Calibration: Standard for calibrating other thermometers
Medical applications: Temperature monitoring in medical equipment

Mnemonic: "Platinum Provides Precise Proportional Resistance"

Question 3(a) OR [3 marks]

Define specific heat and heat capacity. And write its units.

Answer:

Specific Heat: Amount of heat energy required to raise the temperature of 1 kg of substance by 1 K.

Heat Capacity: Amount of heat energy required to raise the temperature of an entire object by 1 K.

Table: Heat Capacity Terms

Term	Formula	SI Unit
Specific Heat (c)	Q = mc∆T	J/(kg·K)
Heat Capacity (C)	Q = C∆T	J/K

Mnemonic: "Specific for Substance, Capacity for Complete Object"

Question 3(b) OR [4 marks]

Explain heat convection in fluid with example.

Answer:

Heat Convection: Transfer of heat through a fluid (liquid or gas) by the movement of the fluid itself.

Process: Hot fluid expands, becomes less dense, rises; cooler fluid descends, creating a continuous circulation pattern called convection current.

Diagram: Convection Current

      ↑      ↑      ↑
    warm    warm   warm
      ^      ^      ^
      |      |      |
   ┌──────────────────┐
   │  heat source     │
   └──────────────────┘
   
       Cool fluid
       ↓      ↓      ↓

Example: Boiling water in a pot - heated water rises to the top while cooler water sinks to the bottom.

Mnemonic: "Heat Rises, Cool Descends, Currents Circulate"

Question 3(c) OR [7 marks]

Define coefficient of thermal conductivity. Derive its equation of coefficient of thermal conductivity for heat transfer in solids.

Answer:

Coefficient of Thermal Conductivity: The amount of heat transferred per unit time per unit area per unit temperature gradient.

Definition: The quantity of heat flowing per second through unit area when temperature gradient is unity.

Derivation:

Consider a rod with cross-sectional area A and length L
Temperature difference between ends is ∆T
Heat flow Q in time t

Heat current = Q/t Temperature gradient = ∆T/L Area = A

According to Fourier's law: Q/t = k·A·(∆T/L)

Rearranging: k = (Q·L)/(t·A·∆T)

Where k is the coefficient of thermal conductivity.

Diagram: Thermal Conductivity

   T₁                 T₂
    ↓                  ↓
┌────────────────────────┐
│                        │ Area A
└────────────────────────┘
    ←───── L ─────→
        Heat flow →

Unit: W/(m·K)

Mnemonic: "Heat Quantity Transfers Along Length Divided by Area and Temperature"

Question 4(a) [3 marks]

Write the difference between transverse waves and longitudinal waves.

Answer:

Table: Transverse vs Longitudinal Waves

Property	Transverse Waves	Longitudinal Waves
Particle motion	Perpendicular to wave direction	Parallel to wave direction
Medium displacement	Crests and troughs	Compressions and rarefactions
Examples	Light waves, water waves	Sound waves, seismic P-waves
Medium requirements	Can travel through solids	Can travel through solids, liquids, gases
Polarization	Can be polarized	Cannot be polarized

Mnemonic: "Transverse Takes Perpendicular Path, Longitudinal Likes Linear Lanes"

Question 4(b) [4 marks]

Calculate the wavelength of a wave having velocity 350 m/s and frequency 10 Hz.

Answer:

Wave Equation: v = fλ

Where:

v is wave velocity (350 m/s)
f is frequency (10 Hz)
λ is wavelength (to be calculated)

Calculation: λ = v/f = 350/10 = 35 m

Mnemonic: "Velocity Values frequency times wavelength"

Question 4(c) [7 marks]

Define Ultrasonic waves and write its characteristics. Write its four major applications of Ultrasonic wave.

Answer:

Ultrasonic Waves: Sound waves with frequencies higher than the upper audible limit of human hearing (above 20 kHz).

Characteristics:

High frequency: Above 20 kHz
Short wavelength: Enables detection of small objects
Directional: Can be focused in a specific direction
Non-ionizing: Safe for biological tissues
Penetration: Can travel through various media

Diagram: Ultrasonic Wave

      Amplitude
        ↑
        │   /\      /\      /\
        │  /  \    /  \    /  \
 ───────┼─/────\──/────\──/────\──────→ Time
        │/      \/      \/      \
        │
      Period < 50 μs (f > 20 kHz)

Applications:

Medical: Diagnostic imaging, therapeutic procedures
Industrial: Non-destructive testing, flaw detection
Cleaning: Ultrasonic cleaning baths for precision parts
Distance measurement: Sonar, parking sensors, level indicators

Mnemonic: "Ultrasonic Uses Sound to Sense, Scan, Sanitize"

Question 4(a) OR [3 marks]

Explain the polarization of light with neat diagram.

Answer:

Polarization: The process of restricting the vibrations of light waves to a single plane.

Types:

Linear polarization
Circular polarization
Elliptical polarization

Diagram: Light Polarization

 Unpolarized Light  Polarizer   Polarized Light
       ↓              ↓             ↓
 ⊥↔↕⊢⊣|↖↗↘↙       ┌─────┐        ↔↔↔↔
 ⊥↔↕⊢⊣|↖↗↘↙  →   │/////│   →    ↔↔↔↔
 ⊥↔↕⊢⊣|↖↗↘↙       └─────┘        ↔↔↔↔
  Multiple         Allows only    Single plane
  vibration        one plane      vibration
   planes

Mnemonic: "Polarizers Pick Particular Planes"

Question 4(b) OR [4 marks]

If velocity of light in air is 3 x 10⁸ m/s and velocity of light in water is 2.25 x 10⁸ m/s. Calculate reflective index of water.

Answer:

Refractive Index Formula: n = c/v

Where:

n is the refractive index
c is the speed of light in vacuum (or air)
v is the speed of light in medium

Calculation: n = 3 × 10⁸ / 2.25 × 10⁸ = 3/2.25 = 4/3 = 1.33

Mnemonic: "Slower Speeds Show higher index"

Question 4(c)(i) OR [4 marks]

Define: velocity, wavelength and frequency of wave. And derive the relationship between wave velocity, wavelength and frequency.

Answer:

Wave Velocity (v): The speed at which a wave travels through a medium.

Wavelength (λ): The distance between two consecutive similar points on a wave.

Frequency (f): Number of complete wave cycles passing a point per unit time.

Diagram: Wave Parameters

Amplitude
    ↑
    │   /\      /\      /\
    │  /  \    /  \    /  \
────┼─/────\──/────\──/────\─→ Distance
    │/      \/      \/      \
    │
    ↑        ↑              ↑
  Wavelength (λ)    Period (T)

Derivation:

In time T (period), the wave travels a distance of one wavelength λ
So, v = λ/T
Since f = 1/T (frequency is inverse of period)
Therefore, v = λf

Mnemonic: "Velocity Values frequency times wavelength"

Question 4(c)(ii) OR [3 marks]

Write properties of light.

Answer:

Table: Properties of Light

Property	Description
Propagation	Travels in straight lines in homogeneous medium
Speed	3 × 10⁸ m/s in vacuum
Reflection	Bounces off surfaces following law of reflection
Refraction	Changes direction when passing between media
Dispersion	White light splits into component colors
Interference	Waves can superimpose to create patterns
Diffraction	Bends around obstacles and through small openings
Polarization	Can be restricted to vibrate in one plane
Dual nature	Exhibits both wave and particle properties

Mnemonic: "Light Reflects, Refracts, Disperses, Interferes, Polarizes"

Question 5(a) [3 marks]

Explain law of refraction of light for plane surface. And explain Snell's law.

Answer:

Law of Refraction: When light passes from one medium to another, it changes direction at the boundary.

Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

n₁sin(θ₁) = n₂sin(θ₂)

Where:

n₁ is the refractive index of first medium
n₂ is the refractive index of second medium
θ₁ is the angle of incidence
θ₂ is the angle of refraction

Diagram: Refraction

           ┌─────────────
   Normal  │
      ↑    │    Medium 1 (n₁)
      │    │
      │    │    Incident ray
      │   /│
      │  / │
      │ /  │
      │/θ₁ │
      ├────┼────────────────
      │\θ₂ │
      │ \  │
      │  \ │
      │   \│    Medium 2 (n₂)
           │    Refracted ray
           │
           │
           └─────────────

Mnemonic: "Sines Show Speeds in Separate Substances"

Question 5(b) [4 marks]

A step index fiber has core refractive index of 1.30 and relative refractive index difference is Δ=0.02. Find numerical aperture.

Answer:

Numerical Aperture Formula: NA = √(n₁² - n₂²)

For step index fiber: NA = n₁√(2Δ)

Where:

n₁ is the core refractive index
Δ is the relative refractive index difference

Calculation: NA = 1.30 × √(2 × 0.02) NA = 1.30 × √0.04 NA = 1.30 × 0.2 NA = 0.26

Mnemonic: "Numerical Aperture Needs core And Delta"

Question 5(c) [7 marks]

Explain Total internal reflection of light. And derive the equation of critical angle.

Answer:

Total Internal Reflection (TIR): The complete reflection of light at the boundary between two media when light travels from a denser medium to a rarer medium at an angle greater than the critical angle.

Conditions for TIR:

Light must travel from denser to rarer medium
Angle of incidence must exceed critical angle

Critical Angle: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

Derivation: Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂)

At critical angle (θc):

θ₁ = θc
θ₂ = 90°
sin(90°) = 1

Therefore: n₁sin(θc) = n₂sin(90°) = n₂ × 1 = n₂

Rearranging: sin(θc) = n₂/n₁

Diagram: Total Internal Reflection

       Medium 1 (n₁)
       (Denser)
       ┌─────────────────
       │  \      /
       │   \θc  /
       │    \  /
       │     \/
       │     /\
       │    /  \
       │   /    \
       │  /      \
       └─────────────────
       Medium 2 (n₂)
       (Rarer)

Mnemonic: "Critical Comes when Dense to Rare with Sine at Ratio"

Question 5(a) OR [3 marks]

Explain numerical aperture and acceptance angle for fiber optic cable.

Answer:

Numerical Aperture (NA): Measure of the light-gathering ability of an optical fiber.

Acceptance Angle (θₐ): Maximum angle at which light can enter the fiber and still experience total internal reflection.

Relationship: NA = sin(θₐ)

Diagram: Numerical Aperture and Acceptance Angle

                 θₐ
                /│\
      Cladding /a│ \    Cladding
      ────────┼──┼──┼────────
              │  │  │
      Core    │  │  │    Core
      ────────┼──┼──┼────────
              │  │  │
      Cladding│  │  │    Cladding
      ────────┴──┴──┴────────

Mnemonic: "Acceptance Angle Allows light, Numerical Aperture Names its Sine"

Question 5(b) OR [4 marks]

Write full form LASER. Write its characteristics.

Answer:

LASER: Light Amplification by Stimulated Emission of Radiation

Table: Characteristics of LASER

Characteristic	Description
Monochromatic	Single wavelength or color
Coherent	All waves in same phase
Highly directional	Travels in straight line with minimal divergence
High intensity	Concentrated energy in narrow beam
Collimated	Parallel rays with minimal spreading

Mnemonic: "LASER Light: Mono, Coherent, Direct, Intense"

Question 5(c) OR [7 marks]

Explain the construction of optical fiber cable in details. And Explain Step index and Graded index optical fiber.

Answer:

Optical Fiber Construction:

Core: Central light-transmitting portion (glass or plastic)
Cladding: Surrounds core, with lower refractive index than core
Buffer Coating: Protective plastic coating
Jacket: Outer protective covering

Diagram: Optical Fiber Structure

      ┌───────────────┐
      │               │ ← Jacket
      │  ┌─────────┐  │
      │  │         │  │ ← Buffer Coating
      │  │  ┌───┐  │  │
      │  │  │   │  │  │
      │  │  │   │  │  │
      │  │  └───┘  │  │
      │  │    ↑    │  │
      │  └────┼────┘  │
      │       │       │
      └───────┼───────┘
              ↑
             Core
            Cladding

Step Index Fiber:

Abrupt change in refractive index between core and cladding
Light travels in zigzag path by total internal reflection
Higher modal dispersion (signal spreading)
Simpler construction

Graded Index Fiber:

Gradual change in refractive index from center of core to cladding
Light travels in helical path due to continuous refraction
Lower modal dispersion
More complex construction

Diagram: Step Index vs Graded Index Fiber

Step Index:
       ─────────────────────
      /                      \
     /    ┌────────────┐     \
    /     │            │      \
   |      │    Core    │      |
    \     │            │     /
     \    └────────────┘    /
      \      Cladding      /
       ────────────────────
       
Graded Index:
       ─────────────────────
      /                      \
     /     ┌──────────┐      \
    /     /            \      \
   |     |     Core     |      |
    \     \            /      /
     \     └──────────┘      /
      \      Cladding       /
       ────────────────────

Refractive Index Profile:

Step Index:           Graded Index:
    │                     │
n₁ ─┤▄▄▄▄▄▄▄              ▄▄▄▄▄
    │       │            ▄     ▄
    │       │           ▄       ▄
n₂ ─┤       ▀▀▀▀▀▀▀    ▄         ▄
    │                  ▀▀▀▀▀▀▀▀▀▀▀
    └───────→ r        └───────→ r

Mnemonic: "Step Shows Sharp Shift, Graded Gradually Goes down"