**Effect of Slip on Rotor Parameters**

**2. Effect of Slip on Magnitude of Rotor Induced E.M.F** We have seen that when rotor is standstill, s = 1, relative speed is maximum and maximum e.m.f. gets induced in the rotor. Let this e.m.f. be,

E

_{2}= Rotor induced e.m.f. per phase on standstill condition As rotor gains speed, the relative speed between rotor and rotating magnetic field decreases and hence induced e.m.f. in rotor also decreases as it is proportional to the relative speed N

_{s}- N. Let this e.m.f. be, E

_{2r}= Rotor induced e.m.f. per phase in running conditionNow E

_{2r }α N_{s}while E_{2r}α N_{s}- N Dividing the two proportionality equations,

E

_{2r}/E_{2}= ( N_{s}- N)/N_{s}but (N_{s}- N)/N = slip s E

_{2r}/E_{2}= s E

_{2r}= s E_{2} The magnitude of the induced e.m.f in the rotor also reduces by slip times the magnitude of induced e.m.f. at standstill condition.

The rotor winding has its own resistance and the inductance. In case of squirrel cage rotor, the rotor resistance is very very small and generally neglected but slip ring rotor has its own resistance which can be controlled by adding external resistance through slip rings. In general let,

R

_{2 }= Rotor resistance per phase onstandstill X

_{2 }= Rotor reactance per phase on standstill Now at standstill, fr = f hence if L

_{2 }is the inductance of rotor per phase, X

_{2 }= 2πfr L_{2 }= 2πf L_{2 }Ω/ph While R

_{2}= Rotor resistance in Ω/ph Now in running condition, f

_{r }= s f hence, X

_{2r }= 2πf_{r }L_{2 }= 2πfs L_{2 }= s .(2πf L_{2}) X

_{2r }= s X_{2 }where X

_{2r }= Rotor reactance in running condition Thus resistance as independent of frequency remains same at standstill and in running condition. While the rotor reactance decreases by slip times the rotor reactance at standstill.

Hence we can write rotor impedance per phase as :

Z

_{2}= Rotor impedance on standstill (N = 0) condition = R

_{2}+ j X_{2}Ω/ph Z

_{2}= √**(**R_{2}^{2}+ X_{2})^{2}**)**Ω/ph ...... magnitude While Z

_{2r}= Rotor impedance in running condition = R

_{2}+ j X_{2r }= R_{2}+ j (s X_{2}) Ω/ph Z

_{2r}= √**(**R_{2}^{2}+ (s X_{2})^{2}**)**Ω/ph ...... magnitude

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