Electric Motor – NTSE Physics Study Notes
Short title – Electric Motor
Exam – National Talent Search Examination (NTSE) – Physics
Target – Class 12 students (or advanced high‑school)
1. Simple Explanation
An electric motor converts electrical energy into mechanical (rotational) energy.
It works on the principle that a current‑carrying conductor in a magnetic field experiences a force (Lorentz force).
By arranging many such conductors in a rotating arrangement and using a magnetic field, the motor produces a continuous torque that turns an axle.
2. Key Points (Bullet Summary)
- Basic Principle – Lorentz force:
[ \mathbf{F}=I(\mathbf{L}\times \mathbf{B}) ] - Major Types
- DC Motors – Brush & commutator; speed directly proportional to applied voltage.
- AC Induction Motors – Two‑pole (synchronous) or multi‑pole (induction) – slip needed for torque.
- Synchronous AC Motors – Rotor field locked to stator frequency; no slip.
- Universal Motors – Work on AC or DC; high speed, low torque.
- Key Components
- Stator (field windings or permanent magnets)
- Rotor (armature windings)
- Commutator & brushes (DC)
- Slip rings (AC induction)
- Important Quantities
- Torque (T) – (T = k \Phi I) (DC) or (T = \dfrac{k \Phi^2 s}{R}) (AC induction).
- Back EMF (E) – (E = k \Phi \omega).
- Speed (N) – (N = \dfrac{V - IR}{k \Phi}) (DC) or (n_s = \dfrac{120 f}{P}) (synchronous).
- Slip (s) – (s = \dfrac{n_s - n_r}{n_s}) (AC induction).
- Power Relationships
[ P_{\text{out}} = T \omega, \qquad P_{\text{in}} = VI, \qquad \eta = \dfrac{P_{\text{out}}}{P_{\text{in}}} ] - Speed Regulation – Change field flux (vary field current) or supply voltage.
- Efficiency – Depends on copper losses, iron losses, mechanical losses.
3. Fundamental Equations
| Quantity | Symbol | Expression | Notes |
|---|---|---|---|
| Angular speed | (\omega) | (2\pi N/60) | (N) in rpm |
| Back EMF | (E) | (k \Phi \omega) | (k) = machine constant |
| Torque (DC) | (T) | (k \Phi I_a) | (I_a) = armature current |
| Torque (AC Induction) | (T) | (\dfrac{k \Phi^2 s}{R_r}) | (R_r) = rotor resistance |
| Slip | (s) | (\dfrac{n_s - n_r}{n_s}) | (n_s) synchronous speed, (n_r) rotor speed |
| Synchronous speed | (n_s) | (\dfrac{120 f}{P}) | (f) = frequency, (P) = poles |
| Power output | (P_{\text{out}}) | (T \omega) | Mechanical power |
| Power input | (P_{\text{in}}) | (V I) | Electrical power |
| Efficiency | (\eta) | (\dfrac{P_{\text{out}}}{P_{\text{in}}}) | Usually 70–95 % |
4. DC Motors – Working
- Armature windings carry current (I_a).
- Field flux (\Phi) (from permanent magnets or field windings).
- Lorentz force on each turn produces torque.
- Commutator reverses current direction every half‑turn → continuous rotation.
- Back EMF opposes applied voltage; determines speed.
Typical Parameters
| Parameter | Symbol | Typical Range |
|---|---|---|
| Applied voltage | (V) | 12 V – 400 V |
| Armature resistance | (R_a) | few ohms |
| Field flux | (\Phi) | 0.01 – 1 Wb |
| Speed (no load) | (N_{0}) | 10^3 – 10^5 rpm |