A 220V dc machine supplies 20A at 200 V as a generator. The armature resistance is 0.2 . If the machine is now operated as a motor as a same terminal voltage and current but with flux increased by 10%, the ratio of motor speed to generator speed is

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  1. 0.87
  2. 0.95
  3. 0.96
  4. 1.06

Answer (Detailed Solution Below)

Option 1 : 0.87
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Detailed Solution

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Concept:

The EMF equation of a DC Machine is

From the above equation,

In a dc generator, induced emf is

Eg = V + IaRa

In a dc motor, back emf is

Eb = V – IaRa

Where,

N is the speed in rpm

ϕ is the flux per pole

P is the number of poles

Z is the number of conductors

V is the terminal voltage

Ia is the armature current

Ra is the armature resistance

Calculation:

Given-

V = 200, Ra = 0.2 Ω, Ia = 20 A, ϕ2 = 1.1 ϕ1

Let ϕ1 = Generator flux, ϕ2 = Motor flux, N1 = Generator speed, N2 = Motor speed 

∴ 

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