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A DC shunt generator has a speed of 800 rpm when delivering 20 A to the load at the terminal voltage of 220 V. If the same machine is run as a motor it takes a line current of 20 A from 220 V supply. The speed of the machine as a motor will be
1. 800 rpm
2. More than 800 rpm
3. Less than 800 rpm
4. Both higher or lower than 800 rpm

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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.

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