AC vs DC Machines

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Questions and Answers

Which of the following factors primarily differentiate AC machines from DC machines?

The presence of an air gap between the stator and rotor.
The use of brushes and commutators in AC machines.
The method used for producing the rotating field and the nature of terminal currents and voltages. (correct)
The type of magnetic materials used in their construction.

AC induction motors utilize a commutator to generate a rotating sinusoidal field.

False (B)

In AC machines, what characteristic of winding configuration is essential for producing a sinusoidal airgap field?

sinusoidally distributed

AC machines are typically supplied by currents and voltages that vary ______ in time.

sinusoidally Signup and view all the answers

Match the following characteristics to whether they primarily apply to AC or DC machines:

Requires a commutator = DC Machines Utilizes sinusoidally varying currents and voltages = AC Machines Produces torque via current and flux density distribution in the air gap = Both AC and DC Machines Signup and view all the answers

What is the primary advantage of using the approximate equivalent circuit of an induction motor (IM) compared to the exact equivalent circuit?

It simplifies calculations and parameter determination from experimental tests. (D) Signup and view all the answers

Given the equation for breakdown slip $s_{po} ≈ \frac{R_r'}{\sqrt{R_s'^2 + (X_r' + X_s')^2}}$, describe how an increase in the rotor resistance ($R_r'$) affects the breakdown torque of an induction motor, assuming other parameters remain constant.

Increasing rotor resistance increases the breakdown torque. Signup and view all the answers

The no-load test on an induction motor is conducted by applying reduced voltage to the machine's terminals to minimize core losses.

False (B) Signup and view all the answers

In the context of induction motors, what does the term 'pull-out torque' refer to?

The maximum torque the motor can produce without stalling. (B) Signup and view all the answers

The stator resistance in an induction motor is typically determined by a DC measurement between any two terminals, and the value is calculated as $R_1 = R_{LL} / _____$, where $R{LL}$ is the measured line-to-line resistance.

2 Signup and view all the answers

For calculating torque at zero speed, which parameters are most crucial in the provided torque equation?

Rotor resistance and slip. (B) Signup and view all the answers

Match the following parameters with the corresponding tests used to determine them in an induction motor:

Stator Resistance ($R_1$) = DC Resistance Test Combined Rotor and Stator Parameters = No-Load Test Signup and view all the answers

Explain why adjusting the DC current to an approximately rated value is important when measuring stator resistance.

To approximate the temperature of the winding under running conditions. Signup and view all the answers

What is the relationship between rotor loss ($P_{loss}$), slip (s), and rotor electromagnetic input ($P_{em}$)?

$P_{loss} = s \times P_{em}$ (C) Signup and view all the answers

In a squirrel cage motor, high rotor resistance is ideal for high full load efficiency.

False (B) Signup and view all the answers

The power input to a slipping clutch is equal to the power transferred from the stator to the rotor at what speed?

synchronous speed Signup and view all the answers

The mechanical output power of a motor is represented by $T_d \omega_r$, from which losses due to ______ and windage must be deducted.

friction Signup and view all the answers

Match the following motor characteristics with their ideal rotor resistance ($R_r'$):

High full load efficiency = Low $R_r'$ High starting torque relative to full load = High $R_r'$ Reduced starting current = High $R_r'$ Signup and view all the answers

What does $P_{mech} = \omega_r T_d = (1 - s)\omega_s T_d$ represent?

Rotor Output (C) Signup and view all the answers

In the slipping clutch analogy, how is the developed torque ($T_d$) calculated?

By dividing the power crossing the air gap ($P_{em}$) by the synchronous speed ($\omega_s$). (C) Signup and view all the answers

Using a wound rotor machine with an external starting resistance is disadvantageous because it increases both cost and maintenance requirements.

True (A) Signup and view all the answers

What does the slip (s) of an induction motor represent?

The normalized difference between the synchronous speed ($N_s$) and the rotor speed ($N_r$) relative to the synchronous speed ($N_s$). (D) Signup and view all the answers

In the steady-state operation of an induction motor, the frequency of the voltage induced in the rotor ($f_r$) is independent of the source frequency ($f$) connected to the stator.

False (B) Signup and view all the answers

In the equivalent circuit of an induction motor, what electrical component represents the power output and torque development resulting from the referred rotor current inducing a speed EMF in the stator?

Rr’(1-s)/s Signup and view all the answers

The rotating magnetic field in an induction motor produces a torque $T_d$ on the rotor, resulting in work done at a rate of $T_d \omega_s$, which represents the __________ power to the rotor.

input Signup and view all the answers

In the steady-state equivalent circuit of an induction motor, which of the following equations correctly represents the relationship involving stator voltage ($V_s$), stator current ($I_s$), stator resistance ($R_s$), stator leakage reactance ($X_s$), stator frequency ($\omega_e$), and induced EMF ($E_s$)?

$V_s = R_s I_s + jX_s \omega_e I_s + E_s$ (D) Signup and view all the answers

In the context of an induction motor's equivalent circuit, what physical phenomenon is represented by the magnetizing reactance ($X_m$)?

The mutual inductance between the stator and rotor windings, representing the air gap flux. (C) Signup and view all the answers

According to the equivalent circuit model, the speed EMF induced in the stator by the rotor currents is at its maximum when the motor operates at synchronous speed (s=0).

False (B) Signup and view all the answers

Match the induction motor parameters to their effect on the motor's equivalent circuit:

Stator Resistance ($R_s$) = Represents the power loss in the stator winding due to the flow of stator current. Rotor Resistance ($R_r'$) = Accounts for the power loss in the rotor winding, referred to the stator side. Stator Leakage Reactance ($X_s$) = Models the voltage drop due to the leakage flux in the stator. Magnetizing Reactance ($X_m$) = Represents the magnetizing current required to establish the magnetic field in the air gap. Signup and view all the answers

What is the primary reason for varying the voltage in proportion to the frequency when controlling an induction motor below its rated frequency?

To keep the magnetizing flux and, thus, $I_m$, constant, ensuring consistent torque capability. (A) Signup and view all the answers

When operating an induction motor with variable frequency and voltage, the torque expression is solely dependent on the slip frequency ($s \omega_e$) for all practical values of slip.

False (B) Signup and view all the answers

In the context of induction motor control, what specific adjustment is made when extended speed operation ($ \omega_e > \omega_{e_rated}$) is required, and what fundamental limitation necessitates this adjustment?

The field must be reduced because the maximum supply voltage to the converter is fixed at $V_{rated}$. Signup and view all the answers

When $V_s = k\omega_e$ is maintained, the motor flux remains approximately ______, simplifying torque control at lower frequencies.

constant Signup and view all the answers

Match the following operating conditions/parameters with their effects on induction motor performance:

Decreasing $\omega_e$ while keeping $V_s$ constant = Increased magnetizing flux, potential saturation Maintaining $V_s/\omega_e$ ratio = Constant magnetizing flux Increasing $\omega_e$ beyond $\omega_{e_rated}$ with fixed $V_s$ = Field weakening, reduced torque capability Operating with very small $s\omega_e$ = Torque expression becomes less accurate Signup and view all the answers

Under what condition is the approximation $ \frac{R_r'}{s\omega_e} \gg \frac{R_s}{\omega_e}$ NOT valid, thus affecting the simplified torque equation?

When the excitation frequency $ \omega_e$ is very small. (C) Signup and view all the answers

A DC-link H-bridge inverter is utilized to supply a constant voltage and constant frequency waveform to the induction motor, optimizing its performance at a fixed operating point.

False (B) Signup and view all the answers

Explain how exceeding the rated excitation frequency ($ \omega_{e_rated}$) impacts the available torque, assuming the supply voltage is limited to $V_{rated}$.

Exceeding the rated excitation frequency reduces the available torque due to field weakening. Since the voltage is capped at $V_{rated}$, increasing $ \omega_e$ decreases the magnetizing flux, which in turn lowers the motor's torque-producing capability. Signup and view all the answers

In a single coil system with a time-varying current $i_a(t)$, what mathematical operation is used to represent the winding MMF, considering only the fundamental component?

Summation of cosine terms with odd harmonics. (D) Signup and view all the answers

If the current $i_a(t)$ in a single coil system is purely sinusoidal, the resulting MMF, $MMF_a(t, \Theta)$, contains higher order harmonics of the spatial angle $ \Theta $.

False (B) Signup and view all the answers

In a balanced three-phase system, the phase difference between any two consecutive phase currents (e.g., $i_a(t)$ and $i_b(t)$) is how many radians?

$\frac{2\pi}{3}$ Signup and view all the answers

In a three-phase winding, assuming sinusoidal winding distribution, the spatial distribution of the number of turns for phase 'a', $N_a(\Theta)$, is proportional to the _________ of the angle $ \Theta $.

cosine Signup and view all the answers

Match the MMF component to its corresponding expression in a three-phase system:

$MMF_a(t, \Theta)$ = $\frac{NI}{2} [sin(\Theta + \omega t) - sin(\Theta - \omega t)] $ $MMF_b(t, \Theta)$ = $\frac{NI}{2} [sin(\Theta + \omega t - \frac{4\pi}{3}) - sin(\Theta - \omega t)] $ $MMF_c(t, \Theta)$ = $\frac{NI}{2} [sin(\Theta + \omega t - \frac{2\pi}{3}) - sin(\Theta - \omega t)] $ Signup and view all the answers

In a three-phase winding system, what causes the field to shift in space?

The phase angle in the current waveforms. (A) Signup and view all the answers

The total MMF ($MMF_T(t, \Theta)$) generated by a balanced three-phase winding system is stationary in space but varies in time.

False (B) Signup and view all the answers

For a three-phase winding with sinusoidal current and winding distributions, the magnitude of the total MMF ($MMF_T(t, \Theta)$) is directly proportional to what parameter?

N*I Signup and view all the answers

The total MMF, $MMF_T(t, \Theta)$, in a three-phase system is given by $\frac{3NI}{2} sin(\omega t - \Theta)$. This equation indicates that the MMF wave is traveling in space with a velocity determined by $ \omega $, which represents the _________ frequency.

angular Signup and view all the answers

What is the key characteristic of the field produced by a balanced three-phase winding, assuming sinusoidal current and winding distributions?

It rotates in space at a constant angular velocity. (C) Signup and view all the answers

Flashcards

AC Machines

Electrical machines that operate with alternating current and produce electromagnetic torque.

Rotating Field Principle

The principle that allows AC machines to produce torque through sinusoidally distributed windings.

Induction Motors

AC machines that generate a rotating magnetic field and convert electrical energy into mechanical energy without needing a commutator.