Correct Answer - Option 1 : 800 rpm
Concept:
EMF (Eg) generated in the shunt generator is given by
Eg = V + IaRa
Where, Ia = Armature current
V = Terminal voltage
Ra = Armature resistance
Rsh = Shunt resistance
Ng = Generator speed
Nm = Motor speed
ϕfg = Generator field flux
ϕfm = Motor field flux
Field current in shunt generator (Ifg) is given by
\({I_{fg}} = \frac{{V}}{{R_{sh}}} \)
Also, Eg ∝ Ngϕfg
Back EMF (Eb) generated in the shunt motor is given by
Eb = V - IaRa
Field current in shunt motor (Ifm) is given by
\({I_{fm}} = \frac{{V}}{{R_{sh}}} \)
Also, Em ∝ Nmϕfm
Analysis:
As there is no series resistance, so no voltage drop
∴ Ifg = Ifm ⇒ ϕfg = ϕfm = ϕ
As there is no series resistance, so no voltage drop (Ra = 0Ω )
Eg = Em = V = 220 V
As E ∝ Nϕ ∝ N (As ϕ is constant )
\(\dfrac{E_g}{E_m}=\dfrac{N_g}{N_m}\)
\(\dfrac{220}{220}=\dfrac{800}{N_m} \)
Nm = 800 rpm
As in the question, there is nothing mention about armature resistance, this implies that if there is no resistive drop then the value of Eb will be same for both motor and generator. This makes the speed of rotor and motor equal. Speed less than 800 rpm will be the wrong answer.