• The speed of a d.c. motor is given by N = (V - Ia Ra)/(k phi), so it depends on the applied voltage V, the armature current Ia, the armature resistance Ra, and the field flux phi.
• Shunt motor: the field flux is nearly constant (the field is connected across the supply). The speed falls only slightly as the load (armature current) increases, because the armature resistance drop (Ia Ra) increases. The shunt motor has a nearly constant speed characteristic.
• Series motor: the field winding is in series with the armature, so the flux is proportional to the armature current (until saturation). As the load increases, the flux increases, so the speed falls sharply. The series motor has a falling speed characteristic and must never be run without load (it would overspeed). Its speed depends strongly on the load.
• The speed can also be varied by changing the applied voltage (armature voltage control) or the field flux (field weakening).

Let each resistor be R and the line voltage be V.

(i) Star:

• Three resistors in star: each phase voltage = V/root 3. Power per resistor = (V/root3)^2/R = V^2/(3R). Total P3 = 3 x V^2/(3R) = V^2/R.
• Two resistors remaining: P2 = 2 x V^2/(3R).
• Reduction = V^2/R - 2V^2/(3R) = V^2/(3R). Fractional reduction = 1/3 = 33.3%.

(ii) Delta:

• Three resistors in delta: each phase voltage = V. Power per resistor = V^2/R. Total P3 = 3V^2/R.
• Two resistors remaining: P2 = 2V^2/R.
• Reduction = 3V^2/R - 2V^2/R = V^2/R. Fractional reduction = 1/3 = 33.3%.

So in both cases the load is reduced by one third (33.3%).