--- title: "DFRT, starting methods and capacitor start-run motor" subject: "Electric Machines II" chapter: 3 key: "semester_5/electric_machines_ii:dfrt-starting-methods-csr" source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/dfrt-starting-methods-csr site: BCT Engineering --- # DFRT, starting methods and capacitor start-run motor Electric Machines II · Chapter 3: Fractional Kilowatt Motors - Asked in: 2078 Kartik, 6 marks - Video: [double revolving field theory of single phase induction motor | double revolving theory](https://www.youtube.com/watch?v=pXmPCSc9di0) — Mind of Engineer - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/dfrt-starting-methods-csr - Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-3 ## Question Explain the double field revolving theory for single phase induction motor. Write starting methods and explain operating principle of the capacitor start and run motor. ## Short answer DFRT resolves a pulsating field into two equal-amplitude counter-rotating fields; at standstill net torque is zero, so the motor is not self-staring. Starting methods: split-phase, capacitor-start, capacitor-start capacitor-run, permanent-split capacitor, shaded-pole. A capacitor-start capacitor-run motor uses a large start capacitor and small run capacitor in the auxiliary winding; a centrifugal switch removes the start capacitor at ~75% speed, giving high starting torque and smooth running. ## Answer #### Double field revolving theory (DFRT) A single-phase winding produces a **pulsating** field $B = B_m\cos\omega t$ along a fixed axis, not a rotating one. DFRT states that this pulsating field can be split into **two fields of half amplitude** ($B_m/2$ each) rotating at synchronous speed in **opposite directions**: $$ B_m \cos\omega t\,\cos\theta = \frac{B_m}{2}\cos(\theta - \omega t) + \frac{B_m}{2}\cos(\theta + \omega t) $$ - The forward field (FF) gives torque $T_f$ in its direction, the backward field (BF) gives $T_b$ in the opposite direction. - At standstill both slips are 1, so $T_f = T_b$ and **net torque is zero**: the motor is not self-starting. - If the rotor is pushed in either direction, the slip w.r.t. that field becomes small, $T_f > T_b$, and the motor keeps running in that direction. ```text T | Tf | /\ | / \___ net T = Tf - Tb --+------------------------------> speed -n |\___ / +n | \ / | \/ Tb ``` #### Starting methods 1. Split-phase (resistance start) motor 2. Capacitor-start induction-run motor 3. Capacitor-start capacitor-run (two-value capacitor) motor 4. Permanent split capacitor (PSC) motor 5. Shaded-pole motor All of them create a second field displaced in space and time so that a rotating field exists at start. #### Capacitor-start capacitor-run (CSCR) motor **Construction:** a main winding and an auxiliary winding displaced by $90^\circ$ electrical. The auxiliary circuit has two capacitors in parallel: a large **electrolytic starting capacitor** $C_s$ in series with a centrifugal switch, and a small **oil-type running capacitor** $C_r$ that stays in circuit. ```text o------+-----------+ | | Main Auxiliary | | | +---+---+ V | | | | C_s C_r | | | | CS | | +---+---+ o------+-----------+ ``` **Operation:** - At start $C_s + C_r$ make $I_a$ lead $I_m$ by nearly $90^\circ$, giving high starting torque ($T_{st} \propto I_m I_a \sin\alpha$). - At about 75% of synchronous speed the centrifugal switch removes $C_s$. - $C_r$ keeps the motor running as a nearly balanced two-phase motor. **Advantages:** high starting torque, high power factor and efficiency, quiet operation. Used in compressors, refrigerators and air-conditioners. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. According to the double field revolving theory, a pulsating field of amplitude B_m is equivalent to: A. Two fields of amplitude B_m rotating in the same direction B. Two fields of amplitude B_m/2 rotating at synchronous speed in opposite directions C. One field of amplitude B_m/2 rotating forward only D. Two fields of amplitude B_m/2 rotating in the same direction at different speeds Answer: B. The pulsating field splits into forward and backward rotating fields, each of half amplitude, both at synchronous speed. (Key point: DFRT statement) 2. Why is the net torque zero at standstill in a single-phase induction motor? A. The rotor has no induced current B. Forward and backward slips are both 1, so T_f = T_b C. The backward field disappears at standstill D. The forward field is weaker than the backward field Answer: B. At standstill both slips equal 1, so the two fields produce equal and opposite torques and the net is zero. (Key point: Zero starting torque) 3. In the capacitor-start capacitor-run motor, what happens at about 75% of synchronous speed? A. The running capacitor is removed and the starting capacitor stays B. The centrifugal switch removes the starting capacitor C_s, leaving C_r in circuit C. The auxiliary winding is completely disconnected D. Both capacitors are disconnected Answer: B. The switch removes only the large starting capacitor; the small running capacitor stays so the motor runs like a balanced two-phase motor. (Key point: CSCR capacitors) 4. Why does the CSCR motor give high starting torque? A. C_s + C_r make I_a lead I_m by nearly 90 degrees, so sin(alpha) is near 1 B. The running capacitor alone makes I_a lag I_m by 90 degrees C. The centrifugal switch increases the supply voltage D. The windings are placed 180 degrees apart Answer: A. T_st is proportional to I_m I_a sin(alpha), and the large capacitance makes alpha close to 90 degrees. 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