SSC JE Electrical Engineering 2017 Set 3 Paper

Speed of a series motor at no load is infinite.${\mathit{E}}_{\mathit{b}}=\mathit{V}-{\mathit{I}}_{\mathit{a}}{\mathit{R}}_{\mathit{a}}$
$\mathit{K}\mathit{\varphi }\mathit{w}=\mathit{V}-{\mathit{I}}_{\mathit{a}}{\mathit{R}}_{\mathit{a}}$
In DC series motors Armature current (${\mathit{I}}_{\mathit{a}}$ ) = Field current (${\mathit{I}}_{\mathrm{f}}$ ) because both armature and field are connected in series then $\mathit{\varphi }\propto {\mathit{I}}_{\mathrm{f}}$
So ${\mathit{I}}_{\mathit{a}}\propto \mathit{\varphi }$
${\mathit{K}}_1{\mathit{I}}_{\mathit{a}}\mathit{w}=\mathit{V}-{\mathit{I}}_{\mathit{a}}{\mathit{R}}_{\mathit{a}}$
∴ $\mathit{w}=\frac{\mathit{V}}{{\mathit{K}}_1{\mathit{I}}_{\mathit{a}}}-\frac{{\mathit{R}}_{\mathit{a}}}{{\mathit{K}}_1}$
So $\mathit{w}\propto \frac{1}{{\mathit{I}}_{\mathit{a}}}$
at no load ${\mathit{I}}_{\mathit{a}}$ = 0, So speed is infinite