Backemf

Back-EMF, short for back electromotive force, is a voltage generated in a conductor or coil when current flows and the magnetic environment changes, or when a coil moves through a magnetic field. According to Faraday’s law and Lenz’s law, the induced emf opposes the change that produced it.

In DC machines, back-EMF is produced when the rotor turns within the stator field. The rotating conductors cut magnetic flux and induce an emf proportional to the rotor speed. This back-EMF adds to the applied voltage, effectively reducing the net voltage across the winding and thus lowering the current as speed rises. At standstill, back-EMF is near zero and the motor draws a large startup current.

The back-EMF magnitude is E_b = K_e ω, where ω is angular velocity and K_e is the motor’s back-EMF constant (in V·s/rad). The torque produced is τ = K_t I, with K_t the torque constant. In SI units, K_t and K_e are related (K_t ≈ K_e). This relation ties electrical input to mechanical output and explains how speed and current interact.

Back-EMF also enables energy recovery when a motor acts as a generator and contributes to motor protection and speed control. In practice, designers consider back-EMF for limiting current, designing controllers, and including protective snubbers to suppress voltage spikes when power is interrupted.