Final answer:
The estimated no-load speed of the shunt DC motor when supplied with 150 V can be approximated as 1350 rpm, provided the magnetization characteristics remain consistent. However, this estimate is based on the loaded speed at 200 V and ignores the armature current, so the actual no-load speed may differ.
Step-by-step explanation:
The speed of a shunt DC motor is proportional to the voltage supplied when the armature winding resistance is negligible. The speed (n) is given by the formula n = V - IaRa / kΦ, where V is the supplied voltage, Ia is the armature current, Ra is the armature resistance (which is negligible in this case), k is a constant, and Φ is the magnetic flux. At no-load, the motor speed will be higher because the armature current (Ia) is minimal. From the given magnetization characteristic equation, Ea = 500If / (2 + If), we can infer the relationship between the field current (If) and the back electromotive force (Ea), which influences the motor's speed.
To calculate the no-load speed at 150 V, we can assume the magnetization characteristics remain consistent and that the changes in supply voltage will scale the speed linearly since Ra is negligible and Φ is constant. The no-load speed at 200 V would be somewhat above 1800 rpm (since Ia is zero and no-load implies no armature current), and so at 150 V (which is (150/200) or 3/4 of 200 V), the no-load speed can be estimated to be 3/4 of the no-load speed at 200 V. Unfortunately, the no-load speed at 200 V is not given, so we cannot calculate the exact figure; thus, we have to use the provided speed of 1800 rpm under load as a reference which can introduce an error as we're ignoring the armature current's effect on speed.
If we simply consider the ratios of the voltages and the given speed, the estimated no-load speed can be approximated as 1350 rpm (which is 3/4 of 1800 rpm). But, without the specific no-load speed at 200 V, this remains an estimation.