# 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 **N _{1}** = 1500 RPM

Armature current at no-load

**I**= 40 A

_{a}Armature Resistance

**R**= 0.3 Ω

_{a}**N**= 1000RPM

_{2}As it is known the torque is constant, thus armature current and flux will also remain constant. The voltage equation can be given as

**E _{b} = V − I_{a}R_{a}**

= 250 − 40 × 0.3

**E _{b} = 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

**E _{b} = V − I_{a}(R_{a} + R_{se})**

152 = 240 − 40 (0.3 + R_{se})

40R_{se} = 76

**R _{se} = 1.9Ω**