The amount of back e.m.f. of a shunt motor will increase when

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When the Field is Weakened

Explanation: In a DC shunt motor, the back e.m.f. ($E_b$) is directly proportional to the magnetic flux ($Phi$) and the speed ($N$). When the field is weakened, the flux decreases; however, the speed of the motor increases significantly, and since the increase in speed is the dominant effect on $E_b$ ($E_b = V - I_a R_a$), the back e.m.f. effectively rises to approach the supply voltage. Working Principle: The relationship is defined by $E_b = \frac{P \Phi Z N}{60 A}$. When the field current is reduced, $\Phi$ drops. To maintain the equilibrium between electrical input and mechanical load, the motor accelerates ($N$ increases). The increase in speed $N$ is proportionally larger than the decrease in flux $\Phi$, leading to an increase in $E_b$. Key Formulas: $E_b = \frac{P \Phi Z N}{60 A}$ — Fundamental equation for Back E.M.F.; $E_b = V - I_a R_a$ — Voltage balance equation for a DC motor Key Points: Back e.m.f. is known as the 'counter e.m.f.' which opposes the applied voltage.; Field weakening is a common method for speed control above rated speed.; As the motor speed increases due to lower flux, the internal generated voltage increases. Advantages: Efficient speed control above base speed.; Maintains high power output during speed adjustment. Disadvantages: Risk of dangerous over-speeding if field circuit breaks.; Reduced torque capacity at higher speeds. Applications: Constant power industrial drives.; Variable speed traction motors. Additional Info: When load increases, the motor slows down, causing $E_b$ to decrease so that more armature current can be drawn.. Option A is incorrect because increasing load increases the armature current, which causes a voltage drop ($I_a R_a$), decreasing the back e.m.f. Answer: B is correct — When the field is weakened, the flux decreases, causing the motor speed to rise sufficiently to increase the back e.m.f. towards the supply voltage. Exam Tip: Always remember that in DC motors, flux and speed are inversely related; thus, any change in flux has an inverse effect on speed, which dictates the back e.m.f. value.

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