DC Motor & Generator
A lumped brushed DC machine model uses one constant k linking magnetic flux linkage to both back-emf (E_b = kω) and torque (τ = kI). Motor mode integrates Jω̇ = kI − bω with V = I R_a + E_b; generator mode fixes shaft speed and computes E = kω and load current from R_a + R_load.
Who it's for: Introductory electromagnetism and energy conversion; complements the moving-magnet induction lab with a rotating-coil picture.
Key terms
- back emf
- DC motor
- generator
- Faraday induction
- Lorentz torque
- Ohm’s law
Live graphs
How it works
A rectangular coil in a uniform magnetic field illustrates the same energy conversion in both directions. With a DC supply, current produces torque and the rotor accelerates until back-emf balances the circuit. When you crank the rotor, motion generates emf and drives current through a load — a dynamo.
Key equations
Frequently asked questions
- Why is the same k used for torque and back-emf?
- For an ideal energy-consistent model in SI units, the same flux linkage per ampere and per rad/s ties electrical and mechanical power: roughly P_elec ≈ E_b I ≈ τω, which forces k to appear in both relations when losses are lumped into R and b.
- Where is the commutator?
- Commutation is implicit: the model assumes torque and induced emf stay aligned so the rotor keeps turning in motor mode and delivers DC polarity into the resistive load in generator mode, as in a simplified textbook brushed machine.
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