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The developed electromagnetic force and/or torque in electromechanical energy conversion systems, acts in a direction that tends to ___________ (i) increase the co-energy at constant flux (ii) increase the co-energy at constant mmf (iii) decrease the stored energy at constant mmf (iv) decrease the stored energy at constant flux Which of the above statements are correct?
(ii), (iv)
(i), (iii)
(ii), (iii)
(i), (iv)
(ii), (iv)
Quick Trick: In electromagnetic systems, force/torque ALWAYS acts to INCREASE co-energy (at constant current/mmf) or DECREASE stored magnetic field energy (at constant flux).
In electromagnetic systems, force/torque ALWAYS acts to INCREASE co-energy (at constant current/mmf) or DECREASE stored magnetic field energy (at constant flux).
Analyze Force/Torque relation at Constant MMF
At constant MMF (current i), mechanical force is derived from the positive derivative of co-energy: F = +(dWco/dx). This means developed torque acts in a direction that tends to INCREASE co-energy (Wco). Statement (ii) is correct.
Analyze Force/Torque relation at Constant Flux
At constant flux linkage (lambda), mechanical force is derived from the negative derivative of stored field energy: F = -(dWfield/dx). This means developed torque acts in a direction that tends to DECREASE stored energy (Wfield). Statement (iv) is correct.
Combine Valid Statements
Matching the derived valid conditions gives statements (ii) and (iv), corresponding directly to Option A.
B: (i) and (iii) state the exact opposite conditions for both flux and mmf. C: (iii) is incorrect because energy decreases at constant flux, not constant mmf. D: (i) is incorrect because co-energy increases at constant mmf, not constant flux.
A is correct because the developed force always acts to increase co-energy at constant mmf and decrease stored energy at constant flux.
Remember the dual nature rule: Co-energy is maximized under independent variable current (MMF), while Field Energy is minimized under independent variable flux linkage.