# A DC motor takes an armature current of 100 A at 440 V. The armature circuit resistance is 0.3 Ω. The machine has 6 poles and armature is lap-connecte

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A DC motor takes an armature current of 100 A at 440 V. The armature circuit resistance is 0.3 Ω. The machine has 6 poles and armature is lap-connected with 822 conductors, the flux per pole is 0.05 wb. Calculate the speed.
1. 598.5 rpm
2. 610 rpm
3. 698 rpm
4. 710 rpm

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Correct Answer - Option 1 : 598.5 rpm

Concept:

The EMF equation of a DC Machine is

${E_b} = \frac{{NPϕ Z}}{{60A}}$

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 = 440 V

Ia = 100 A

Ra = 0.3 Ω

P = 6

A = P = 6 (LAP winding)

Z = 822

ϕ = 0.05 wb

Eb = V – IaRa

Eb = 440 - 100 × 0.3 = 410 V

${E_b} = \frac{{NPϕ Z}}{{60A}}\Rightarrow N =\frac{E_b\times 60\times A}{Pϕ Z}$

$N = \frac{410 \times 60 \times6 }{6\times 0.05\times 822}=598.54\;rpm$

∴ The speed is 598.5 rpm

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