# A 240 V DC series motor takes 40 A when giving its rated output at 1500 RPM. Its resistance is 0.3 Ω. The value of resistance that must be added to obtain rated torque at 1000 rpm is

A 240 V DC series motor takes 40 A when giving its rated output at 1500 RPM. Its resistance is 0.3 Ω. The value of resistance that must be added to obtain rated torque at 1000 rpm is

### Right Answer is: 1.9Ω

#### SOLUTION

Supply Voltage V = 300 V
Rated Speed N1 = 1500 RPM
Armature current at no-load Ia = 40 A
Armature Resistance Ra = 0.3 Ω
N2 = 1000RPM

As it is known the torque is constant, thus armature current and flux will also remain constant. The voltage equation can be given as

Eb = V − IaRa

=  250 − 40 × 0.3

Eb = 228 V

At constant flux

$\begin{array}{l}\dfrac{N}{{{N_o}}} = \dfrac{{{E_b}}}{{{E_{bo}}}}\\\\{E_{b2}} = \dfrac{{{N_2}}}{{{N_1}}} \times {E_{b1}}\\\\ = \dfrac{{1000}}{{1500}} \times 228\\\\{E_{b2}} = 152V\end{array}$

Now the Back EMF of DC series Motor is given by

Eb = V − Ia(Ra + Rse)

152 = 240 − 40 (0.3 + Rse)
40Rse = 76

Rse = 1.9Ω

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