The dynamo and the DC motor

Explain in your own words what electromagnetic induction is: what the three requirements are for generating a voltage in a conductor and what happens if there is no relative motion between the conductor and the magnetic field.

A bicycle dynamo powers the lights by pressing against the wheel. Explain where the electrical energy it produces really comes from and why you notice more resistance when pedalling while the dynamo is connected.

The brighter the bicycle light powered by a dynamo shines, the harder it is to pedal. Explain this relationship using the conservation of energy: the electrical energy coming out of the dynamo must enter from somewhere.

Match each part of a DC motor to its function: (1) stator, (2) rotor, (3) split-ring commutator, and (4) brushes, with: (a) stationary part that creates the magnetic field; (b) rotating part containing the coils; (c) segmented cylinder that reverses the current at the right moment; (d) sliding contacts that supply current to the moving part.

Explain what problem the commutator-brush assembly solves in a DC motor: how current reaches a rotating part and why its direction must be reversed every half turn so that the torque does not stop.

The figure shows a schematic cross-section of a DC motor. The two identical parts marked with "?" are located next to the commutator.

1. a) Explain the function of the labeled parts of the motor: housing (stator), magnet, rotor, commutator and shaft.

1. b) Identify the two parts marked with "?" and explain their function in the motor.

1. c) Explain which forces make the rotor turn and why the commutator must reverse the current every half turn.

A direct current motor is powered at $12\ \text{V}$ and draws $3\ \text{A}$.

1. a) Calculate the electrical power it absorbs, $P = V \cdot I$.

1. b) Explain what this value means and how this power is divided between the two destinations it has in a motor.

A motor absorbs $100\ \text{W}$ from the mains and delivers $80\ \text{W}$ of mechanical power at its shaft.

1. a) Calculate its efficiency, $\eta = \frac{P_{util}}{P_{abs}} \cdot 100$.

1. b) Calculate the power that is lost and explain what it is transformed into.

A cordless drill is powered by a $18\ \text{V}$ battery and consumes $5\ \text{A}$ at full load, with an efficiency of $75\ \%$. (a) Calculate the electrical power absorbed. (b) Calculate the useful mechanical power at the drill bit, $P_{util} = \eta \cdot P_{abs}$, expressing the efficiency as a decimal. (c) Calculate the power lost and reason why the casing heats up during use.

The diagram represents the rated power balance of a DC motor supplied at a constant voltage of $24\ \text{V}$. During a test on the test bench at full load, an internal armature resistance of $R_i = 0{,}8\ \Omega$ is measured.

(a) Quantify the total flow of losses ($?$) and break it down quantitatively by calculating the power dissipated by the Joule effect in the winding versus the remaining stray losses (mechanical and iron losses).

(b) After an extended test without forced ventilation, the armature copper heats up, rising from $20\ ^\circ\text{C}$ to $70\ ^\circ\text{C}$ (temperature coefficient $\alpha = 0{,}00393\ ^\circ\text{C}^{-1}$). Predict the new value of the power lost through the Joule effect if the motor continues to draw the same $100\ \text{W}$ of electrical input power, and calculate how the overall efficiency changes.

(c) A student claims that if the mechanical load is reduced so that the motor delivers only $40\ \text{W}$ of useful power, the efficiency will remain $80\ \%$, since "losses are cut in half". Refute this statement by distinguishing between fixed and variable losses in a DC electrical machine.

The figure shows the chain of energy transformations from pedalling to a bicycle light, with one stage covered by a question mark, as shown in the figure.

(a) Identify the machine and the form of energy in the stage marked with the question mark. (b) Explain why there is an output of heat to the surroundings and which law guarantees that all the energy from pedalling ends up in one of the two outputs. (c) Reason what would happen to the pedalling effort if the light bulb were disconnected.

A direct current motor connected to a $12\ \text{V}$ line vertically lifts a $20\ \text{kg}$ load at a constant speed of $0{,}2\ \text{m/s}$ while drawing $4\ \text{A}$ ($g = 9{,}8\ \text{m/s}^2$). The internal resistance of the armature is known to be $R_i = 0{,}4\ \Omega$.

(a) Determine the overall electromechanical efficiency of the system and break down the power losses: calculate how much power is dissipated by Joule effect in the armature winding and how much corresponds to the remaining losses (mechanical friction and magnetic losses).

(b) An operator claims that if the load mass is tripled ($60\ \text{kg}$), the motor will consume exactly triple the current ($12\ \text{A}$) and lift it at the same speed. Reasonably refute this claim by analyzing how the back electromotive force ($E'$) and the rotational speed vary with the increase in load torque in a DC motor.

(c) Calculate the current that the motor would draw if the load were to jam, stalling the rotor ($n = 0$), and justify what immediate consequences this would have for the integrity of the winding if a circuit breaker does not trip in time.

For the winch of a light industrial hoist, a motor-gearbox unit must be selected capable of vertically lifting a $40\ \text{kg}$ load at a constant linear speed of $0{,}3\ \text{m/s}$ ($g = 9{,}8\ \text{m/s}^2$). The cable is wound on a $10\ \text{cm}$ diameter drum coupled to the output shaft of a gear reducer with a mechanical efficiency of $80\ \%$. Two commercial DC motors are available:

• Motor A: Rated voltage $12\ \text{V}$, rated current $10\ \text{A}$, rotational speed $2400\ \text{rpm}$, electromechanical efficiency of $65\ \%$.

• Motor B: Rated voltage $24\ \text{V}$, rated current $9\ \text{A}$, rotational speed $1800\ \text{rpm}$, electromechanical efficiency of $75\ \%$.

(a) Determine the useful mechanical power that must be delivered by the motor shaft to lift the load at the required speed, taking into account the losses in the reducer. Justify which of the two motors is viable for this application.

(b) For the selected motor, calculate the gear ratio $i = \omega_{\text{motor}} / \omega_{\text{drum}}$ required in the reducer and the rated useful torque (in $\text{N}\cdot\text{m}$) that this motor delivers at its own shaft.

(c) If an installer mistakenly mounts the discarded motor while maintaining the same gear ratio calculated in section (b), predict whether the system will be able to lift the load at rated conditions and analyze the thermal and operational consequences for that motor.