SOLUTION

Supply Voltage V = 300 V
Rated Speed N₁ = 1500 RPM
Armature current at no-load I_a = 40 A
Armature Resistance R_a = 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

E_b = V − I_aR_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