Motor Back-EMF
Voltage a spinning motor generates against its supply.
Formula
Variables
Example
k_e=0.05, ω=200: V_b = 10 V
How it works
A motor spinning in its own magnetic field behaves like a generator, so its rotating conductors induce a voltage that opposes the applied supply voltage. That induced voltage is proportional to angular speed, which is why the back-EMF increases as the motor spins faster. The constant k_e depends on the motor’s construction and units, linking mechanical speed to electrical output through electromagnetic induction.
When to use it
Use this relation when analyzing DC motors, brushless motors, or motor drivers to estimate the internal opposing voltage at a given speed. It is especially useful for finding current draw, stall behavior, speed control limits, and checking whether a supply voltage is sufficient for a target RPM.
Worked example, step by step
Given: k_e = 0.018 V·s/rad, ω = 750 rad/s Step 1: Write the formula: V_b = k_e ω Step 2: Substitute the values: V_b = 0.018 × 750 Step 3: Multiply: V_b = 13.5 Final answer: V_b = 13.5 V
Common mistakes to avoid
- Using RPM directly instead of converting to rad/s first
- Confusing the back-EMF constant k_e with torque constant values without checking units
- Forgetting that back-EMF opposes the supply, so it reduces the effective voltage across the windings
Did You Know?
Back-EMF rises with speed until it nearly cancels the supply — which sets a motor's no-load top speed.
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