Step 1: Understanding the Problem:
This question explores the relationship between the field excitation and speed of a DC shunt motor under running conditions.
Step 2: Key Formula or Approach:
The speed ($N$) of a DC motor is given by the speed equation:
\[ N = \frac{E_b}{k \Phi} \]
where:
$E_b$ = Back EMF
$\Phi$ = Magnetic flux per pole
$k$ = Motor constant
Step 3: Detailed Explanation:
• In a DC shunt motor, the field winding is connected in parallel with the armature across the voltage supply, providing a constant flux.
• If the field winding suddenly opens while the motor is running, the shunt field current drops to zero.
• The magnetic flux ($\Phi$) in the machine does not immediately drop to absolute zero, but falls to a very low value determined only by the residual magnetism ($\Phi_{res}$) of the magnetic pole cores.
• According to the speed relation $N \propto \frac{1}{\Phi}$, when the flux becomes extremely small, the speed must increase dramatically to maintain the back EMF ($E_b = V - I_a R_a$).
• As the speed attempts to rise toward infinity, the motor enters a "runaway" condition.
• This dangerously high speed can lead to catastrophic mechanical failure of the armature due to massive centrifugal forces.
Step 4: Final Answer
Thus, the motor will attain a dangerously high speed, corresponding to option (C).