How is a DC motor typically modeled in DC circuit analysis for steady-state?

How is a DC motor typically modeled in DC circuit analysis for steady-state?

• A. As a pure resistor
• B. As a series LC network
• C. As a dependent source in parallel with a resistor
• D. As a resistor with back-EMF; in simple models, a series RL with a back-emf source that reduces current

Answer: (D)

The key idea is that a running DC motor generates back-EMF, a voltage opposed to the applied voltage. In steady-state DC analysis, this back-EMF reduces the net voltage across the windings, which lowers the current. The practical model is a winding resistance in series with a back-EMF source (often written as V = I R + E_b, where E_b = K_e ω). In simple models, you may see a series RL with back-EMF to also reflect winding inductance, but inductive effects don’t affect the steady-state current once things have settled. This structure captures how the motor’s speed sets the back-EMF, which in turn limits current and sets torque (torque being proportional to current). Therefore, representing the motor as a resistor with a back-EMF in series best matches steady-state DC circuit analysis.

The key idea is that a running DC motor generates back-EMF, a voltage opposed to the applied voltage. In steady-state DC analysis, this back-EMF reduces the net voltage across the windings, which lowers the current. The practical model is a winding resistance in series with a back-EMF source (often written as V = I R + E_b, where E_b = K_e ω). In simple models, you may see a series RL with back-EMF to also reflect winding inductance, but inductive effects don’t affect the steady-state current once things have settled. This structure captures how the motor’s speed sets the back-EMF, which in turn limits current and sets torque (torque being proportional to current). Therefore, representing the motor as a resistor with a back-EMF in series best matches steady-state DC circuit analysis.