SSC JE Electrical Engineering 2012 Paper

Electro magnetic torque
$\mathit{T}=\mathit{K}{\mathit{\varphi }}_1\cos \mathit{\varphi }$
where k is designed constant = (PZ/2πA)
where
P = number of poles
Z = Total number of amature conductor
N = rotation speed of the armature in revolution per minute (r.p.m.)
A = number of parallel paths
Now the flux ϕ is increased by 100% i.e.
${\mathit{\varphi }}_2={\mathit{\varphi }}_{\mathit{j}}+100\%{\mathit{\varphi }}_1=2{\mathit{\varphi }}_1$
${\mathit{I}}_2=0.75{\mathit{I}}_1$
${\mathit{T}}_1\propto {\mathit{\varphi }}_1{\mathit{I}}_1\cos 45°$ &
${\mathit{T}}_2\propto {\mathit{\varphi }}_2{\mathit{I}}_2\cos 30°$ &
${\mathit{T}}_2\propto {\mathit{\varphi }}_2{\mathit{I}}_2\cos 30°$ $=2{\mathit{\varphi }}_1\times 0.75{\mathit{I}}_1\times \cos 30°$
$\frac{{\mathit{T}}_1}{{\mathit{T}}_2}=\frac{1\times \cos 45°}{2\times 0.75\times \cos 30°}$ = 0.544
$\Rightarrow {\mathit{T}}_1=0.544{\mathit{T}}_2$
Then ${\mathit{T}}_2=1.838$, ${\mathit{T}}_1=183.7\%\mathrm{of}{\mathit{T}}_1$
Hence, the Torque increases to 183.7% of the original.