# DC Motor Problem I am really confused with the above problem. The equations which I was able to write are

Ea1 = Vt - RseIa1 = kphi1*wm1

Ea2 = Vt - 0.5*RseIa2 = kphi2*wm2

phi1*Ia1 = phi2*Ia2 [Torque is constant]

First Approach - Assuming shunt field is strong.So, phi doesn't change much

phi1=phi2

Ia1=Ia2

Ea2 > Ea1

So, wm2>wm1 [option B]

Second Approach - Assuming series field has appreciable contribution to net flux

phi1 = Nsh*(Vt/Rsh) + Nse*Ia1

phi2 = Nsh*(Vt/Rsh) + Nse*Ia2*0.5

Now, there are more variables than equations. So how to conclude. Please help me with the above problem.

• 1. Please read how to write the equations, as they can't be understood in actual representation. 2. I guess only the prof knows the answer. If the motor already spins at rated torque, then it is already constant. – Marko Buršič Jan 18 '18 at 11:07
• I opt for a). The excitation field weakens, then the armature field has to rise to produce the same torque. $M\propto I_a\cdot I_f$ – Marko Buršič Jan 18 '18 at 11:16

$$V=k\cdot (I_{sh}+I_{ser})\cdot\Omega+ R_a\cdot I_a$$ $$M=k\cdot (I_{sh}+I_{ser})\cdot I_a$$ $$k\cdot (I_{sh}+I_{ser1})\cdot I_{a1} = k\cdot (I_{sh}+I_{ser2})\cdot I_{a2}$$ $$\dfrac{I_{a2}}{I_{a1}}=\dfrac{I_{sh}+I_{ser1}}{I_{sh}+I_{ser1}\cdot 0.5}$$