SSC JE Electrical Engineering 2015 Paper

For a DC Shunt Motor, field current is practically constant and thus the Torque is directly proportional to a mature current (Ia)
$\mathit{T}=\mathit{K}\mathit{\Phi }{\mathit{I}}_{\mathit{a}}$
$\mathit{T}\propto {\mathit{I}}_{\mathit{a}}$
$\mathit{E}=\mathit{K}\mathit{\Phi }\mathit{\omega }$
$\mathit{V}=\mathit{E}+{\mathit{I}}_{\mathit{a}}{\mathit{R}}_{\mathit{a}}$
$\mathit{E}=\mathit{V}\mathit{–}{\mathit{I}}_{\mathit{a}}{\mathit{R}}_{\mathit{a}}=\mathit{K}\mathit{\Phi }\mathit{\omega }$
$\mathit{\omega }=\frac{\mathit{V}}{\mathit{K}\mathit{\Phi }}-\frac{{\mathit{I}}_{\mathit{a}}{\mathit{R}}_{\mathit{a}}}{\mathit{K}\mathit{\Phi }}$
So if load in increase the speed will flightly reduce