Answer MET Question 44

Question 150:  Derive torque equation of a d.c motor.

Answer: Flemming's LHR

$\displaystyle \small \mathrm{E_b\times I_a = \frac{2\pi NT}{60}}$

torque:

$\displaystyle \small \mathrm{T=\frac{E_b\times I_a\times 60}{2\pi N}}$

We know

$\displaystyle \small \mathrm{E_b = \frac{\phi ZNP}{60A}}$

thus

$\displaystyle \small \mathrm{T = \frac{\phi ZNP}{60A}\times \frac{60I_a}{2\pi N}}$

or

$\displaystyle \small \mathrm{T = \frac{ZP}{2\pi A}\times \phi I_a}$

or $\displaystyle \small \mathrm{T\ \ \alpha \ \phi I_a}$