DC Machines and AC Rotating Machines
Scope
DC Machines and AC Rotating Machines tests DC generator and motor action, back emf, torque, machine types, induction motor synchronous speed, slip, and synchronous machine speed.
Core rules
- DC generator emf: E = ΦZNP/(60A), where P is poles, Z is conductors, N is rpm and A is parallel paths.
- DC motor: Eb = V − IaRa; the back emf opposes the supply and limits armature current.
- Torque is proportional to ΦIa. A shunt motor should not be started with its field open.
- Induction motor synchronous speed: Ns = 120f/P. Slip s = (Ns − Nr)/Ns, and rotor frequency = sf.
- A synchronous motor runs at exactly Ns and can supply leading reactive power when over-excited.
Worked example
A 4-pole induction motor is supplied at 50 Hz and runs at 4% slip. Ns = 120 × 50/4 = 1500 rpm. Nr = Ns(1 − s) = 1500 × 0.96 = 1440 rpm. Rotor frequency = 0.04 × 50 = 2 Hz. The slip is small at normal load but never zero in an induction motor; if it were zero, there would be no rotor emf and no torque.
Traps
- Using 2 poles in the synchronous-speed formula when the machine has 4.
- Adding slip instead of subtracting it from Ns.
- Treating back emf as the terminal voltage of a motor.
- Forgetting that an induction motor’s rotor speed is below synchronous speed.