Question

Consider a dc motor with armature voltage = 125 v and armature resistance = 0.4 ohm. It is running at 1800 rpm under no load condition. The rated armature current is 30
a. Calculate the rated speed of the motor. 1500 rpm 1800 rpm 1627 rpm 900 rpm

Answer 1

"Given:

Voltage (V) = 125 v

Armature resistance = 0.4 ohm

Speed (n1) = 1800 rpm

Current (I1) = 30 A

To find:

Rated speed (n2) = ?

Formula:

$\left( \frac { n1 }{ n2} \right) \quad =\quad \left( \frac { b1 }{ b2} \right)$

$b\quad =\quad V\quad -\quad IR$

Solution:

$Back\quad emf, \quad b\quad =\quad V\quad -\quad IR$

With no load condition, $b1\quad =\quad V\quad -\quad { I }_{ 0 }R$

$b1\quad =\quad 125\quad -\quad \left( 0\quad \times \quad 0.4 \right)$

$b1\quad =\quad 125\quad V$

When current is 30 A, $b2\quad =\quad V\quad -\quad { I }_{ 1 }R$

$b2\quad =\quad 125\quad -\quad \left( 30\quad \times \quad 0.4 \right)$

$b2\quad =\quad 113\quad V$

Now,

$\left( \frac { n1 }{ n2} \right) \quad =\quad \left( \frac { b1 }{ b2}\right)$

$n2\quad =\quad \left( \frac { b2 }{ b1}\right) \quad \times \quad n1$

$n2\quad =\quad \left( \frac { 113 }{ 125 }\right) \quad \times \quad 1800$

$n2\quad =\quad 1627.2\quad rpm\quad =\quad 1672\quad rpm$"

Answer 2

"Given:

Armature Voltage (v) = 125 v

Armature Resistance (R) = 0.4 Ω

Speed (N1) = 1800 rpm

Armature current (I) = 30 A

To Find:

Rated Speed (N2)

Solution:

Formula:

$(\frac{N1}{N2}) = (\frac{B1}{B2})$

B = V – IR

With no load condition,

 B1 = V – IR = 125 – $(0 \times 0.4)$= 125 v

When the armature current is 30 A,

 B2 = V – IR = 125 – $(30 \times 0.4)$ = 113 v

W.K.T

 $(\frac{N1}{N2}) = (\frac{B1}{B2})$

$N2 =\frac{ B2}{B1} \times N1$

$N2 = \frac{113}{125} \times 1800$

N2 = 1627 rpm. Thus the correct option is C."