Shunt motor speed from no load to load

With constant supply voltage, the shunt field current and flux stay constant, so $N \propto E_b$.

Given: $V = 250$ V, $R_a = 1\ \Omega$, $R_{sh} = 125\ \Omega$; no load: $I_{L0} = 5$ A, $N_0 = 1500$ rpm; load: $I_L = 25$ A.

Field current

$$I_{sh} = \frac{250}{125} = 2\ \text{A}$$

No-load (running light)

$$\begin{aligned} I_{a0} &= 5 - 2 = 3\ \text{A} \\ E_{b0} &= 250 - 3 \times 1 = 247\ \text{V} \end{aligned}$$

On load

$$\begin{aligned} I_a &= 25 - 2 = 23\ \text{A} \\ E_b &= 250 - 23 \times 1 = 227\ \text{V} \end{aligned}$$

Speed on load

$$N = N_0 \times \frac{E_b}{E_{b0}} = 1500 \times \frac{227}{247} = 1378.5\ \text{rpm}$$

(Armature reaction is neglected, so flux is taken as unchanged.)

Answer: Speed at 25 A $\approx 1378.5$ rpm.