हिंदी
Maharashtra State BoardHSC Science (Electronics) 12th Standard Board Exam
प्रश्न पत्र२५४
पाठ्यपुस्तक उत्तर१०४७७
MCQ ऑनलाइन अभ्यास परीक्षा६०
महत्वपूर्ण प्रश्न एवं उत्तर७८४१
अवधारणा स्पष्टीकरण और वीडियो७९३
समय सारणी३५
पाठ्यक्रम

A.C. Generator

Advertisements

Topics

Estimated time: 15 minutes
CBSE: Class 12
CISCE: Class 10

Definition: A.C. Generator

An a.c. generator is a device which converts the mechanical energy into the electrical energy using the principle of electromagnetic induction.

CBSE: Class 12

Principle

Whenever the magnetic flux linked with a closed coil changes with time, an electromotive force (EMF) is induced in it. This is Faraday's Law of Electromagnetic Induction.

Faraday's Law (Mathematical Form):

ε = −N × (dΦB / dt)

  • The negative sign indicates Lenz's Law — the induced EMF opposes the change in flux.
  • In an A.C. generator, rotation of the coil in a uniform magnetic field causes a continuous change in flux, thereby inducing a continuously alternating EMF.
CBSE: Class 12

Components & Construction

Labels required:

  • Armature Coil (N turns, Area A)
  • Magnetic Field B (arrows from N to S)
  • Slip Rings (R₁ and R₂)
  • Carbon Brushes (B₁ and B₂)
  • External Load/Resistance
  • Rotor Shaft

Components Table

  Component Material Function
1 Armature Coil Insulated copper wire on an iron core Rotates in field B; site of EMF induction
2 Field Magnet Permanent magnet or electromagnet Provides a uniform magnetic field B
3 Slip Rings Copper/brass (2 rings) Maintain continuous contact between the rotating coil and the brushes
4 Carbon Brushes Carbon (2 brushes: B₁, B₂) Press against slip rings; carry current to the external circuit
5 Rotor Shaft Steel Holds an armature; connected to a mechanical energy source
6 External Load Resistance R Receives and utilises the alternating current
CBSE: Class 12

Working

  • Mechanical energy is supplied to the rotor shaft (steam, water from a dam, wind, etc.)
  • The armature coil rotates in a uniform magnetic field B with constant angular speed ω
  • The angle θ between area vector A of the coil and B changes: θ = ωt
  • This causes the magnetic flux through the coil to change continuously
  • By Faraday's Law, changing flux induces an alternating EMF
  • Current reverses direction every half rotation
  • Slip rings allow continuous rotation while maintaining electrical contact
  • Alternating current (AC) flows in the external load
CBSE: Class 12

Mathematical Derivation of EMF

Step 1: Magnetic Flux at Time t

At t = 0, the coil is perpendicular to B (flux is maximum). At time t:

  • θ = ωt
  • ΦB = BA cos(ωt) [for one turn]

Total flux linkage (N turns): NΦB = NBA cos(ωt)   ...(1)

Step 2: Apply Faraday's Law

  • ε = −d(NΦB)/dt
    = −d/dt [NBA cos(ωt)]
    = −NBA × [−ω sin(ωt)]

∴ ε = NBAω sin(ωt)   ...(2)

Step 3: Peak EMF

EMF is maximum when sin(ωt) = ±1 → θ = 90° or 270°

  • ε₀ = NBAω   ...(3)

Therefore:

  • ε = ε₀ sin(ωt)   ...(4) ← STANDARD FORM

Step 4: In Terms of Frequency

Since ω = 2πn:

  • ε = NBA(2πn) sin(2πnt)   ...(5)

Step 5: Instantaneous Current

  • I = ε/R = (ε₀/R) sin(ωt) = I₀ sin(ωt)   ...(6)

where I₀ = ε₀/R (peak current)

CBSE: Class 12

Example

Kamla pedals a stationary bicycle (like a gym cycle). The pedals are connected to a 100-turn coil that rotates inside a magnetic field. The question asks: What is the maximum voltage (peak EMF) the coil generates?

Given Values

Quantity Symbol Value
Number of turns N 100
Area of coil A 0.10 m²
Frequency of rotation n 0.5 rev/s (half a revolution per second)
Magnetic field B 0.01 T

What Is Being Found?

The maximum (peak) EMF is the highest voltage the rotating coil can generate.

Formula Used

ε0 = NBAω = NBA(2πn)
This is because the coil rotates with angular speed ω = 2πn, and peak EMF occurs when sin⁡(ωt) = 1.
ε0​ = 100 × 0.01 × 0.10 × 2π × 0.5
ε0 ​= 100 × 0.01 × 0.10 × 3.14
ε0 = 0.314 V

Key Takeaway

This example illustrates that even a simple human-powered bicycle can act as an AC generator — just on a very small scale. The low output (0.314 V) is because:

  • The coil rotates very slowly (only 0.5 Hz)
  • The magnetic field is weak (0.01 T)

In real power stations, N, B, A, and ω are all much larger, which is why generators there produce voltages in the kilovolt range (e.g., 11 kV to 33 kV).

CBSE: Class 12

Real-Life Applications

Application Energy Source How a Generator Is Used
Thermal Power Plant Coal → Steam Steam rotates the turbine connected to the armature
Hydroelectric Plant Falling water Water rotates turbine blades
Nuclear Power Plant Nuclear fuel (U-235) Heat → Steam → Turbine → Generator

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Series 3


Series 4


Series 5


Shaalaa.com | Magnetic Effects of Current part 12 (Electric Generator)

Shaalaa.com


Next video


Shaalaa.com


Magnetic Effects of Current part 12 (Electric Generator) [00:13:42]
S
Series: series 1
0%


Magnetic Effects of Current part 12 (Electric Generator)
00:13:42  undefined
Electric Generator
00:14:22  undefined

Related QuestionsVIEW ALL [54]

The given figures 1 to 3 show the working of a simple A.C. generator. Study the diagrams and answers of the following questions.

(i) State and explain the principle underlying the working of a simple generator.
(ii) Where is the loop of wire placed?
(iii) What happens when the loop is rotated?
(iv) Indicate the direction of the current flow through the wire for the first half of the turn (in first figure). Name and state the rule used in finding the direction of the current.
(v) Indicate the direction of the current for the case shown in second figure. 
(vi) Indicate the direction of current in the outer circuit (i.e., electric bulb) in first and third figure.
(vii) What type of current is shown in the above diagrams? Explain.

State whether the following statement is true or false.

An electric motor converts mechanical energy into electrical energy.

 State the principle of an electric generator.

The device used for producing electric current is called a ______.

Observe the figure and write the answers to the questions asked.

  1. The construction shown in the figure is of which device?
  2. Explain the principle on which this device works.
  3. Write any three uses of this device.

In an a.c. generator the speed at which the coil rotates is doubled. How would this affect

  1. the frequency of output voltage,
  2. the maximum output voltage is doubled.

Explain the construction and working of the following. Draw a neat diagram and label it.

Electric Generator (AC)

State whether the following statement are true of false: 

A miniature circuit breaker (MCB) works on the heating effect of current.

Advertisements
Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×