Question

A DC series motor has linear magnetization and negligible armature resistance. The motor speed is

• A. Directly proportional to $\sqrt{T}$
• B. Directly proportional to T
• C. Inversely proportional to T
• D. Inversely proportional to $\sqrt{T}$

Answer 1

The correct option is D Inversely proportional to $\sqrt{T}$

For series motor, $T\to$ Torque
$T\propto I_a^2$
or, $I_a\propto \sqrt{T}...\left(i\right)$
and also, $E_b\propto N\varphi$
or $E_b\propto N{I}_a$ (as $\varphi \propto I_a$ )
$N\propto \frac{E_b}{I_a}$
From equation (i),
$N\propto \frac{E_b}{\sqrt{T}}$