--- title: "Double field theory; starting methods" subject: "Electrical Machine" chapter: 7 key: "semester_4/electrical_machine:dfrt-two-starting-methods" source: https://www.bctengineer.com/q/semester_4/electrical_machine/dfrt-two-starting-methods site: BCT Engineering --- # Double field theory; starting methods Electrical Machine · Chapter 7: Fractional Kilowatt Motors - Asked in: 2069 Poush - Video: [#Electrical Machines-II | L42 | Starting Methods (Types of 1-ɸ Induction Motor)](https://www.youtube.com/watch?v=2dVIh2wyOtw) — Shivanand Shakya - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machine/dfrt-two-starting-methods - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-7 ## Question Explain double revolving field theory. Explain any two methods which are used for starting single phase induction motor. ## Short answer Pulsating field = two half-magnitude fields rotating oppositely; net torque zero at standstill. Starting: split-phase (high-resistance auxiliary winding creates phase difference) and capacitor-start (series capacitor provides near-90° phase shift for high torque). ## Answer A single-phase winding carrying a.c. produces a pulsating (alternating) field, φ = φ_m cos ωt, along a fixed axis. It does not rotate. The double revolving field theory says that such a pulsating field is equal to two rotating fields of half the magnitude, turning in opposite directions at synchronous speed. #### Resolution of the pulsating flux $$\phi_m\cos\omega t = \frac{\phi_m}{2}e^{j\omega t} + \frac{\phi_m}{2}e^{-j\omega t}$$ i.e. the sum of two vectors, each of length φ_m/2: - forward field φ_f = φ_m/2, rotating at +N_s (say anticlockwise) - backward field φ_b = φ_m/2, rotating at −N_s (clockwise) ```text ωt = 0 ωt = 90° ωt = 180° ff and fb ff and fb point ff and fb both both point opposite ways, at point the other along +axis: 90° to the axis: way along the axis: sum = φm sum = 0 sum = -φm ff = fb = φm/2, turning in opposite directions; resultant = φm cos ωt along the fixed axis ``` The components at right angles to the axis cancel at every instant, and the components along the axis add to give φ_m cos ωt. #### Working of the motor Let the rotor turn in the forward direction at speed N. The slip with respect to the forward field is s_f = (N_s − N)/N_s = s. The slip with respect to the backward field is s_b = (N_s + N)/N_s = 2 − s Each field induces rotor currents and develops its own torque, T_f (forward) and T_b (backward). The net torque is T = T_f − T_b. | Condition | Slip f / b | Result | |---|---|---| | Standstill (s = 1) | 1 / 1 | T_f = T_b, so net torque is zero | | Rotor started forward | s / 2 − s | T_f > T_b, net forward torque | | Rotor near N_s (s → 0) | ~0 / ~2 | T_f large, T_b small | ```text Torque | | ffffff | fffff f | ffffff ********f | fffffffffff **** *f | fffffffffffffffffffffff **** *f |f ****** --+b*------------------------*****------------------------*f> N | ****** b | b* **** bbbbbbbbbbbbbbbbbbbbbbb | b* **** bbbbbbbbbbb | b******** bbbbbb | b bbbbb | bbbbbb | -Ns 0 +Ns f = Tf (forward field), b = Tb (backward field, acting in reverse) * = net torque T = Tf - Tb: zero at N = 0, positive for forward running, and zero again just below +Ns ``` The net torque is zero at standstill, so the single-phase induction motor has no starting torque. If the rotor is given a push in either direction, it keeps rotating in that direction, since the torque of the field rotating that way (T_f or T_b) becomes larger than the other. Near synchronous speed the backward torque is small, because the slip 2 − s for the backward field is near 2: the rotor current it causes is at nearly twice the supply frequency, lags heavily and gives little torque. The net torque falls to zero at a speed slightly below N_s, so the motor never reaches N_s. #### Starting methods **1. Split-phase (resistance-start) motor.** The stator carries a main winding (low R, high L) and an auxiliary winding (high R/X ratio, thin wire), 90° apart in space and connected in parallel. The currents I_m and I_a differ in phase by about 30° to 40°, so a rotating field is produced and the motor starts. A centrifugal switch disconnects the auxiliary winding at about 75 to 80 % of synchronous speed. The starting torque is about 1.5 to 2 times full-load torque. Used in fans, blowers and grinders. **2. Capacitor-start motor.** A capacitor is connected in series with the auxiliary winding and the centrifugal switch. The auxiliary current leads the voltage, and the angle between I_m and I_a approaches 90°, giving a high starting torque (3 to 4.5 times full-load torque) with a lower starting current. The auxiliary winding and capacitor are cut out after starting. Used for compressors, refrigerators and pumps. ```text Supply --+-- Main winding ---------+-- +-- Aux -- C -- Switch ---+ ``` Another method is the shaded-pole motor, in which copper rings on part of each pole delay the flux in that part of the pole, giving a weak field that moves from the unshaded to the shaded part (used for small fans, up to about 50 W). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. At standstill, the net torque of a single-phase induction motor is zero because: A. the backward field is much weaker than the forward field B. T_f = T_b since both slips are 1 C. the rotor current is zero D. the stator winding is open Answer: B. Equal fields and equal slip of 1 give equal and opposite torques. (Key point: Backward field and standstill torque) 2. A rotor turning forward with slip s has what slip with respect to the backward field? A. 2 - s B. s C. 1 + s^2 D. 1 - s Answer: A. s_b = (N_s + N)/N_s = 2 - s. (Key point: Slip with respect to the backward field) 3. How does a split-phase motor produce a starting torque? A. A capacitor in the main winding B. A high-R/X auxiliary winding 90° in space gives a current phase difference of about 25° to 30° with the main winding C. Shorting the rotor bars D. Reversing the supply polarity Answer: B. The two windings are 90° apart in space and their currents are out of phase in time, which creates a rotating field. (Key point: Split-phase starting) 4. Compared with the split-phase motor, the capacitor-start motor has: A. lower starting torque and higher starting current B. higher starting torque (3 to 4.5 times full load) and lower starting current C. the same starting torque but is used for fans only D. no auxiliary winding Answer: B. The capacitor brings I_a and I_m close to 90°, giving a high starting torque at a lower starting current. 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