The resistive component of the rotor with resistance R2 offered to the backward rotating flux wave in a single-phase motor runs with slip s is given as

• A. R2 ⁄ S
• B. R2 ⁄ (1 + S)
• C. R2 ⁄ (1 − S)
• D. R2 ⁄ (2 − S)

Answer: (D)

The flux rotating in the clockwise direction (i.e. the direction of spinning) is called the forward rotating flux (φf) and that in the other direction is called the backward rotating flux (φb). The forward rotating flux has synchronous speed Ns (= 120 f/P) and the synchronous speed of rotating backward flux (anticlockwise) is –Ns.
Slip in forward Direction:-
Sf =  (Ns – N)/Ns = s
Slip in backward Direction:-
Sb =  (–Ns – N)/–Ns = s
Sb =  (2Ns + Ns + N)/Ns
Sb = (2 – s)
At standstill, N = 0 so that Sf = Sb = 1. For forward rotating flux, the slip is s (less than 1) and for backward rotating flux, the slip is 2 – s (greater than 1). We know that in a 3-phase induction motor, the torque developed is directly proportional to effective rotor resistance.
The effective rotor resistance for single-phase motor is R2/s in the forward direction and R2/2 – s in the backward direction.