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PEC EPE Mechatronics study materials
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PEC EPE Mechatronics practice questions

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Question 1Engineering Mathematics and Basic Sciences

In phasor analysis of a mechatronic drive, an impedance is given as Z = 3 + 4j Ω. What is the magnitude of this impedance?

  1. 7 Ω
  2. 5 Ω Correct answer.
  3. 25 Ω
  4. √7 Ω

Explanation

The magnitude of a complex impedance a + bj is √(a² + b²). Substituting a = 3 and b = 4 gives √(9 + 16) = √25 = 5 Ω.

Question 2Engineering Mathematics and Basic Sciences

The displacement of a cam follower is modelled by s(t) = sin(t²). What is the velocity ds/dt?

  1. 2t cos(t²) Correct answer.
  2. −2t cos(t²)
  3. cos(t²)
  4. 2t sin(t²)

Explanation

Differentiating sin(t²) requires the chain rule: the derivative of sin(u) is cos(u), and the derivative of u = t² is 2t. Therefore ds/dt = 2t cos(t²).

Question 3Engineering Mathematics and Basic Sciences

A planar robot linkage uses the transformation matrix M = [[4, 3], [2, 1]]. What is det(M)?

  1. −10
  2. −2 Correct answer.
  3. 10
  4. 2

Explanation

For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc. Here det(M) = (4)(1) − (3)(2) = 4 − 6 = −2.

Question 4Engineering Mathematics and Basic Sciences

A first-order sensor response is modelled by dy/dt = 3y. What is the general solution?

  1. y = C e^{t/3}
  2. y = 3t + C
  3. y = C e^{−3t}
  4. y = C e^{3t} Correct answer.

Explanation

The differential equation dy/dt = ky has the general solution y = C e^{kt}. Here k = 3, so the solution is y = C e^{3t}.

Question 5Engineering Mathematics and Basic Sciences

Two independent safety sensors are fitted to a machine. Sensor A works with probability 0.9 and sensor B works with probability 0.8. What is the probability that at least one sensor works?

  1. 0.80
  2. 0.90
  3. 0.98 Correct answer.
  4. 0.72

Explanation

For independent sensors, P(at least one works) = 1 − P(both fail). The failure probabilities are 0.1 and 0.2, so the result is 1 − (0.1)(0.2) = 0.98.

Question 6Engineering Mathematics and Basic Sciences

A control signal is f(t) = e^{−2t} for t ≥ 0. What is its Laplace transform F(s)?

  1. 1/(s + 2) Correct answer.
  2. 1/(s − 2)
  3. 1/(s² + 4)
  4. 2/s

Explanation

The standard Laplace transform pair is L{e^{at}} = 1/(s − a). With a = −2, this becomes 1/(s + 2), valid for s > −2.

Question 7Engineering Mathematics and Basic Sciences

A microcontroller solves f(x) = 0 using the Newton–Raphson method. Which expression gives the next iterate x_{n+1}?

  1. x_n + f(x_n)/f'(x_n)
  2. x_n + f'(x_n)/f(x_n)
  3. x_n − f'(x_n)/f(x_n)
  4. x_n − f(x_n)/f'(x_n) Correct answer.

Explanation

Newton–Raphson uses the tangent line to f at x_n and solves for its x-intercept. This gives x_{n+1} = x_n − f(x_n)/f'(x_n), provided f'(x_n) is not zero.

Question 8Engineering Mathematics and Basic Sciences

A two-degree-of-freedom mechanical model has the matrix A = [[2, 1], [1, 2]]. What is the smaller eigenvalue of A?

  1. 0
  2. 4
  3. 1 Correct answer.
  4. 2

Explanation

The characteristic equation is det(A − λI) = (2 − λ)² − 1 = 0, giving λ = 3 or λ = 1. The smaller eigenvalue is therefore 1.

Question 9Engineering Mathematics and Basic Sciences

A robot end-effector position in the plane is r(t) = t² i + t³ j, with position in metres and time in seconds. What is the magnitude of its acceleration at t = 1 s?

  1. 6 m/s²
  2. 40 m/s²
  3. 8 m/s²
  4. 2√10 m/s² Correct answer.

Explanation

Differentiate twice: r''(t) = 2i + 6t j. At t = 1, the acceleration vector is 2i + 6j, whose magnitude is √(2² + 6²) = √40 = 2√10 m/s².

Question 10Engineering Mathematics and Basic Sciences

A balanced star-connected three-phase motor is supplied from a 400 V line. What is the phase voltage approximately?

  1. 400 V
  2. 231 V Correct answer.
  3. 200 V
  4. 692 V

Explanation

In a balanced star connection, the line voltage is √3 times the phase voltage. Therefore the phase voltage is 400/√3 ≈ 231 V.

Question 11Engineering Mathematics and Basic Sciences

A planar robot applies transformation A = [[2, 1], [0, 1]] and then transformation B = [[1, 0], [3, 1]] to a point. Which matrix represents the combined transformation B A?

  1. [[2, 1], [3, 4]]
  2. [[2, 3], [1, 4]]
  3. [[5, 2], [3, 1]]
  4. [[2, 1], [6, 4]] Correct answer.

Explanation

For successive transformations, the combined matrix is BA because the rightmost matrix acts first. Multiplying B by A gives row-by-column entries: (1·2+0·0)=2, (1·1+0·1)=1, (3·2+1·0)=6, (3·1+1·1)=4.

Question 12Engineering Mathematics and Basic Sciences

Two force vectors F1 = 3i + 4j N and F2 = 4i − 3j N act on a machine element. What is the scalar product F1 · F2?

  1. 25 N²
  2. 7 N²
  3. 24 N²
  4. 0 N² Correct answer.

Explanation

The scalar product is (3)(4) + (4)(−3) = 12 − 12 = 0 N². A zero dot product means the two force vectors are perpendicular.

Question 13Engineering Mathematics and Basic Sciences

A vibration sensor on a mechatronic test rig produces a signal with frequency content up to 400 Hz. According to the Nyquist criterion, what is the minimum sampling frequency required to avoid aliasing?

  1. 400 Hz
  2. 100 Hz
  3. 200 Hz
  4. 800 Hz Correct answer.

Explanation

The Nyquist criterion requires a sampling frequency greater than twice the highest signal frequency. For 400 Hz, the minimum is 2 × 400 Hz = 800 Hz; exactly 800 Hz is the theoretical lower bound.

Question 14Engineering Mathematics and Basic Sciences

A velocity profile measured on a machine slide is v(0)=0 m/s, v(1)=3 m/s and v(2)=4 m/s. Using the trapezoidal rule with these three equally spaced points, what is the estimated distance travelled from t=0 to t=2 s?

  1. 6 m
  2. 5 m Correct answer.
  3. 4 m
  4. 7 m

Explanation

With h=1 s, the trapezoidal rule gives distance ≈ (h/2)[v0 + 2v1 + v2]. Substituting yields 0.5[0 + 2·3 + 4] = 0.5[10] = 5 m.

Question 15Engineering Mathematics and Basic Sciences

A second-order mechatronic position control system has the characteristic equation s² + 6s + 25 = 0. What is the damping ratio ζ of the system?

  1. 1.2
  2. 0.5
  3. 0.6 Correct answer.
  4. 0.3

Explanation

Comparing with the standard form s² + 2ζωn s + ωn² = 0 gives ωn² = 25, so ωn = 5 rad/s, and 2ζωn = 6. Therefore ζ = 6/(2×5) = 0.6.

Question 16Engineering Mathematics and Basic Sciences

A cable production line has on average 2 defects per 100 m. Assuming a Poisson distribution, what is the probability of exactly zero defects in a 100 m length?

  1. 1 − e^(−2) ≈ 0.865
  2. 0.5
  3. 2e^(−2) ≈ 0.271
  4. e^(−2) ≈ 0.135 Correct answer.

Explanation

For a Poisson distribution with mean λ=2, P(X=0)= e^(−λ) λ^0/0! = e^(−2) ≈ 0.135. This is the probability of no defects in the stated length.

Question 17Engineering Mathematics and Basic Sciences

A signal has Laplace transform F(s) = (3s + 2)/(s² + 5s + 6). What is the initial value f(0+) according to the initial value theorem?

  1. 6
  2. 0
  3. 3 Correct answer.
  4. 2

Explanation

The initial value theorem states that f(0+) = lim_{s→∞} sF(s) when the limit exists. Here sF(s) = (3s² + 2s)/(s² + 5s + 6), whose limit as s→∞ is 3.

Question 18Engineering Mathematics and Basic Sciences

A continuous-time signal x(t) = sin(200πt) + sin(300πt) is sampled at 250 Hz. Which statement correctly describes the aliasing?

  1. Both components alias to 50 Hz.
  2. The 100 Hz component aliases to 150 Hz.
  3. No aliasing occurs because both component frequencies are below the sampling frequency.
  4. The 150 Hz component aliases to 100 Hz and coincides with the 100 Hz component. Correct answer.

Explanation

The components are at 100 Hz and 150 Hz. With fs=250 Hz, the Nyquist frequency is 125 Hz, so the 150 Hz component folds to |150−250|=100 Hz, overlapping the 100 Hz component.

Question 19Engineering Mathematics and Basic Sciences

A force of 50 N is applied perpendicular to a wrench handle at a distance of 0.2 m from the pivot. What is the magnitude of the moment about the pivot?

  1. 25 N·m
  2. 50 N·m
  3. 100 N·m
  4. 10 N·m Correct answer.

Explanation

Moment magnitude is force times perpendicular distance, M = F d. Thus M = 50 N × 0.2 m = 10 N·m.

Question 20Engineering Mathematics and Basic Sciences

A 10 Ω resistor in a mechatronic drive circuit carries a sinusoidal current i(t) = 2 sin(100t) A. What is the average power dissipated in the resistor?

  1. 20 W Correct answer.
  2. 40 W
  3. 14.1 W
  4. 10 W

Explanation

The RMS current is I_rms = 2/√2 = √2 A. Average power is P = I_rms² R = (√2)² × 10 = 20 W.

Question 21Engineering Mathematics and Basic Sciences

A mechatronic controller stores a configuration value as the hexadecimal byte 0x2F. What is its decimal equivalent?

  1. 49
  2. 43
  3. 47 Correct answer.
  4. 45

Explanation

Hexadecimal 0x2F equals 2×16 + 15 = 32 + 15 = 47 in decimal. Each hex digit is weighted by a power of 16, with F representing 15. The conversion is direct for a two-digit hexadecimal byte.

Question 22Engineering Mathematics and Basic Sciences

Two resistors of 6 Ω and 3 Ω are connected in parallel in a sensor signal-conditioning circuit. What is the equivalent resistance?

  1. 9 Ω
  2. 4.5 Ω
  3. 2 Ω Correct answer.
  4. 1.5 Ω

Explanation

For two parallel resistors, R_eq = (R1 R2)/(R1 + R2) = (6×3)/(6+3) = 18/9 = 2 Ω. The equivalent resistance is always smaller than the smallest branch resistance. The 9 Ω value would apply only for a series connection.

Question 23Engineering Mathematics and Basic Sciences

A robot arm bracket carries a normal force of 200 N over a contact area of 0.004 m². What is the average normal stress?

  1. 20 kPa
  2. 8 kPa
  3. 50 kPa Correct answer.
  4. 800 kPa

Explanation

Stress is force divided by area: σ = F/A = 200 N / 0.004 m² = 50,000 Pa. Since 1 kPa = 1,000 Pa, this equals 50 kPa. The result is a normal stress because the force acts perpendicular to the area.

Question 24Engineering Mathematics and Basic Sciences

A force F = 10j N acts at position r = 0.2i + 0.1j m on a machine element. What is the moment of the force about the origin?

  1. 1k N·m
  2. −2k N·m
  3. −1k N·m
  4. 2k N·m Correct answer.

Explanation

The moment is M = r × F. With r = 0.2i + 0.1j and F = 10j, the cross product gives (0.2)(10)k = 2k N·m; the j-component of r does not contribute because j × j = 0. Thus the moment is 2 N·m counter-clockwise about the positive z-axis.

Question 25Engineering Mathematics and Basic Sciences

A closed-loop mechatronic system has characteristic polynomial s³ + 4s² + 5s + K. Using the Routh–Hurwitz criterion, for what range of K is the system stable?

  1. 0 < K < 5
  2. K > 20
  3. 0 < K < 20 Correct answer.
  4. all positive values of K

Explanation

The Routh array first column gives 1, 4, (20 − K)/4, and K. For stability all first-column entries must be positive, so K > 0 and 20 − K > 0. Combining these inequalities gives 0 < K < 20.

Question 26Engineering Mathematics and Basic Sciences

A mechatronic position signal y(t) has Laplace transform Y(s), initial position y(0), and initial velocity y'(0). What is L{y''(t)}?

  1. s²Y(s) − y'(0)
  2. s²Y(s) − s y(0) − y'(0) Correct answer.
  3. sY(s) − y(0)
  4. s²Y(s) + s y(0) + y'(0)

Explanation

Differentiating twice in the time domain introduces two initial-condition terms in the Laplace domain. The standard result is L{y''} = s²Y(s) − s y(0) − y'(0). The first derivative term subtracts s y(0), and the second subtracts y'(0).

Question 27Engineering Mathematics and Basic Sciences

A current sensor outputs i(t) = 10 sin(100t + 30°) A. What is the RMS value of this current?

  1. 5.0 A
  2. 7.07 A Correct answer.
  3. 8.66 A
  4. 10 A

Explanation

For a sinusoid i(t) = I_m sin(ωt + φ), the RMS value is I_m/√2. Here I_m = 10 A, so I_rms = 10/√2 ≈ 7.07 A. The phase angle does not affect the RMS magnitude.

Question 28Engineering Mathematics and Basic Sciences

A velocity signal is sampled at x = 0, 1, and 2 s with values 1, 4, and 9 m/s. Using Simpson's 1/3 rule with the three points, what is the estimated integral over 0 to 2 s?

  1. 9.33 m
  2. 6.67 m
  3. 8.67 m Correct answer.
  4. 8.00 m

Explanation

Simpson's 1/3 rule for two equal subintervals is (h/3)[f0 + 4f1 + f2]. With h = 1, f0 = 1, f1 = 4, and f2 = 9, the integral is (1/3)(1 + 16 + 9) = 26/3 ≈ 8.67 m. This parabolic estimate differs from the trapezoidal value of 9 m.

Question 29Engineering Mathematics and Basic Sciences

A safety-critical mechatronic component has an exponential time-to-failure distribution with a mean time to failure of 5,000 hours. What is the probability that it survives at least 2,000 hours?

  1. 0.3297
  2. 0.6703 Correct answer.
  3. 0.8187
  4. 0.4000

Explanation

For an exponential failure distribution, the survival function is R(t) = e^{−t/MTTF}. Here t/MTTF = 2000/5000 = 0.4, so R = e^{−0.4} ≈ 0.6703. Thus about 67% survive beyond 2,000 hours.

Question 30Engineering Mathematics and Basic Sciences

A linear mechatronic model is described by A = [[1, 2], [3, 4]] and b = [5, 11]. What is the solution vector x in Ax = b?

  1. [1, 2] Correct answer.
  2. [3, −1]
  3. [−1, 3]
  4. [2, 1]

Explanation

The determinant is det(A) = (1)(4) − (2)(3) = −2. Using the inverse or elimination, x = [1, 2] satisfies 1·1 + 2·2 = 5 and 3·1 + 4·2 = 11. Substitution confirms the unique solution.

Question 31Engineering Mathematics and Basic Sciences

A linear actuator's position is given by s(t) = 2t³ − 3t² + 4t, where s is in metres and t in seconds. What is the acceleration of the actuator at t = 1 s?

  1. 8 m/s²
  2. 4 m/s²
  3. 12 m/s²
  4. 6 m/s² Correct answer.

Explanation

Acceleration is the second derivative of position. Differentiating s(t)=2t³−3t²+4t twice gives a(t)=12t−6. Substituting t=1 s yields a=6 m/s².

Question 32Engineering Mathematics and Basic Sciences

A voltage phasor in a mechatronic sensor circuit is given in polar form as 10∠45°. What is its rectangular form?

  1. 8.66 + j5.00
  2. 7.07 + j7.07 Correct answer.
  3. 10.0 + j10.0
  4. 5.00 + j8.66

Explanation

The rectangular form is obtained from V = |V|(cos θ + j sin θ). For 10∠45°, both 10 cos 45° and 10 sin 45° equal approximately 7.07. Thus the rectangular form is 7.07 + j7.07.

Question 33Engineering Mathematics and Basic Sciences

A sensor calibration record shows a standard deviation of 0.05 V. What is the variance of the calibration data?

  1. 0.0500 V²
  2. 0.0250 V² Correct answer.
  3. 0.0005 V²
  4. 0.0025 V²

Explanation

Variance is the square of the standard deviation. Squaring 0.05 V gives (0.05)² = 0.0025 V². This is the variance of the calibration data.

Question 34Engineering Mathematics and Basic Sciences

A mechatronic thermal system is modelled by dT/dt + 2T = 10 with initial condition T(0) = 0. What is the solution T(t) for t ≥ 0?

  1. 10(1 − e^(−2t))
  2. 10e^(−2t)
  3. 5(1 − e^(−2t)) Correct answer.
  4. 5e^(−2t)

Explanation

Write the equation as dT/dt + 2T = 10 and use the integrating factor e^(2t). Integrating gives T e^(2t) = 5e^(2t) + C, so T(t) = 5 + C e^(−2t). Applying T(0)=0 yields C=−5, hence T(t)=5(1−e^(−2t)).

Question 35Engineering Mathematics and Basic Sciences

What is the inverse Laplace transform of F(s) = 1/(s² + 4s + 13)?

  1. (1/3)e^(−2t) sin(3t) Correct answer.
  2. e^(−2t) sin(3t)
  3. (1/3)e^(2t) sin(3t)
  4. e^(−2t) cos(3t)

Explanation

Complete the square in the denominator: s²+4s+13 = (s+2)²+9. The standard transform 1/[(s+a)²+ω²] corresponds to (1/ω)e^(−at) sin(ωt). With a=2 and ω=3, the inverse is (1/3)e^(−2t) sin(3t).

Question 36Engineering Mathematics and Basic Sciences

A 2×2 matrix used in a mechatronic state model is A = [[3, 1], [1, 3]]. What are the eigenvalues of A?

  1. 2 and 4 Correct answer.
  2. 0 and 4
  3. 3 and 3
  4. 1 and 3

Explanation

The characteristic equation is det(A−λI)=0, giving (3−λ)²−1=0. Solving (3−λ)²=1 yields 3−λ=±1, so the eigenvalues are λ=2 and λ=4.

Question 37Engineering Mathematics and Basic Sciences

A production line has a 10% defective rate. Assuming a binomial distribution, what is the probability of exactly 2 defective items in a sample of 5?

  1. 0.0081
  2. 0.3280
  3. 0.0729 Correct answer.
  4. 0.00001

Explanation

The binomial probability is P(X=k)=C(n,k)p^k(1−p)^(n−k). Here n=5, k=2, p=0.1, so P = C(5,2)(0.1)²(0.9)³ = 10×0.01×0.729 = 0.0729.

Question 38Engineering Mathematics and Basic Sciences

A force F = 4i − j N acts at position r = 2i + 3j m on a machine element. What is the moment of the force about the origin?

  1. 14k N·m
  2. 10k N·m
  3. −14k N·m Correct answer.
  4. −10k N·m

Explanation

The moment is the cross product r × F. For r=2i+3j and F=4i−j, the cross product is (2)(−1) − (3)(4) = −2 − 12 = −14, directed along k. Thus the moment is −14k N·m.

Question 39Engineering Mathematics and Basic Sciences

Use one iteration of the Newton–Raphson method with initial guess x0 = 1 to approximate a root of f(x) = cos x − x. What is x1?

  1. 0.750 Correct answer.
  2. 1.250
  3. 0.500
  4. 0.250

Explanation

Newton–Raphson uses x1 = x0 − f(x0)/f′(x0). Here f(1)=cos1−1≈−0.4597 and f′(1)=−sin1−1≈−1.8415. Thus x1 = 1 − (−0.4597)/(−1.8415) ≈ 0.750.

Question 40Engineering Mathematics and Basic Sciences

A measurement error has the probability density function f(x) = k(1 − x²) for −1 < x < 1, and f(x)=0 otherwise. What is the value of k?

  1. 3/4 Correct answer.
  2. 1/2
  3. 2/3
  4. 1

Explanation

A probability density must integrate to 1 over its support. Compute ∫ from −1 to 1 of k(1−x²) dx = k[x − x³/3] from −1 to 1 = k(4/3). Setting k(4/3)=1 gives k=3/4.

Question 41Electrical, Electronic and Embedded Systems

A pick-and-place gripper must detect a metal workpiece through a 2 mm plastic cover and must ignore plastic parts. Which sensing principle is best suited to this task?

  1. Piezoelectric vibration sensor
  2. Thermocouple mounted beside the workpiece
  3. Inductive proximity sensor Correct answer.
  4. Resistive strain gauge bonded to the gripper jaw

Explanation

Inductive proximity sensors create an alternating magnetic field and detect eddy-current losses in a conductive target, so they sense metal through a non-metallic cover without contact. Capacitive sensors would also respond to the plastic cover and are not selective for metal in this task.

Question 42Electrical, Electronic and Embedded Systems

An 8-bit ADC has a 5.0 V full-scale reference and an input range from 0 V to 5.0 V. Ignoring offset and gain errors, what is the nominal LSB size?

  1. 4.88 mV
  2. 9.77 mV
  3. 39.1 mV
  4. 19.5 mV Correct answer.

Explanation

The nominal LSB size equals the full-scale range divided by the number of code intervals, 5.0 V / 2^8 = 5.0 V / 256 ≈ 19.5 mV. Offset and gain errors would modify the actual transfer curve but not this ideal step size.

Question 43Electrical, Electronic and Embedded Systems

In a microcontroller-based mechatronic system, what is the main purpose of a hardware interrupt?

  1. To service an asynchronous event with low latency Correct answer.
  2. To convert an analog sensor channel into a digital code
  3. To retain calibration constants after power is removed
  4. To raise the CPU clock frequency during burst computation

Explanation

A hardware interrupt causes the CPU to suspend normal instruction flow and enter an interrupt service routine when an event occurs. This gives low-latency response without requiring the main program to poll the event continuously.

Question 44Electrical, Electronic and Embedded Systems

An op-amp is connected as a non-inverting amplifier with a 90 kΩ feedback resistor from output to inverting input and a 10 kΩ resistor from inverting input to ground. A 0.20 V DC signal is applied to the non-inverting input. Assuming an ideal op-amp, what is the output voltage?

  1. 1.8 V
  2. 2.2 V
  3. 0.2 V
  4. 2.0 V Correct answer.

Explanation

For a non-inverting amplifier the closed-loop gain is 1 + Rf/Rin = 1 + 90 kΩ/10 kΩ = 10. The output is therefore 10 × 0.20 V = 2.0 V.

Question 45Electrical, Electronic and Embedded Systems

A 24 V DC motor is driven by an H-bridge with a 20 kHz PWM signal at 30% duty cycle. Neglecting switching losses and motor inductance effects, what is the average voltage applied to the motor?

  1. 4.8 V
  2. 16.8 V
  3. 24.0 V
  4. 7.2 V Correct answer.

Explanation

With ideal PWM drive, the motor sees the supply voltage during the on-time and approximately zero during the off-time. The average voltage is therefore duty cycle × supply = 0.30 × 24 V = 7.2 V.

Question 46Electrical, Electronic and Embedded Systems

On an I²C bus, which signal condition defines a START condition?

  1. SDA transitions from high to low while SCL is high Correct answer.
  2. SDA transitions from low to high while SCL is high
  3. SDA toggles while SCL is low
  4. SCL transitions from low to high while SDA is low

Explanation

An I²C START is defined by SDA changing from high to low while SCL remains high; a STOP is the opposite transition. Data bits are allowed to change only while SCL is low so that the high period is stable.

Question 47Electrical, Electronic and Embedded Systems

A first-order RC low-pass filter uses R = 10 kΩ and C = 10 nF. What is the approximate −3 dB cutoff frequency?

  1. 159 Hz
  2. 1.59 kHz Correct answer.
  3. 15.9 kHz
  4. 100 kHz

Explanation

For a first-order RC low-pass filter, the −3 dB cutoff is fc = 1/(2πRC). Substituting 10 kΩ and 10 nF gives fc ≈ 1/(6.283 × 10^-4 s) ≈ 1.59 kHz.

Question 48Electrical, Electronic and Embedded Systems

In a microcontroller, which memory type is volatile and normally holds the stack, local variables, and run-time data during program execution?

  1. EEPROM
  2. Ferroelectric RAM (FRAM)
  3. Static RAM (SRAM) Correct answer.
  4. Flash memory

Explanation

SRAM is volatile, fast, and used for the stack, local variables, and run-time data in a microcontroller. Flash and EEPROM retain data without power, while FRAM is also non-volatile.

Question 49Electrical, Electronic and Embedded Systems

A stepper motor has a step angle of 1.8° and is driven with 16× microstepping. How many microstep pulses are required to rotate the shaft through 90°?

  1. 200
  2. 400
  3. 800 Correct answer.
  4. 1600

Explanation

The motor needs 90°/1.8° = 50 full steps for a quarter turn. At 16× microstepping, each full step is divided into 16 microsteps, so 50 × 16 = 800 pulses are required.

Question 50Electrical, Electronic and Embedded Systems

A mixed-signal PCB contains a sensitive 16-bit ADC front end and a microcontroller with fast digital outputs. Which grounding practice best reduces digital switching noise coupling into the analog measurement?

  1. Partition analog and digital grounds and join them at one point near the ADC Correct answer.
  2. Leave the analog ground floating to isolate it from the digital supply
  3. Connect analog and digital grounds only through a 10 Ω resistor in series with each digital signal
  4. Use a single global ground plane and route digital return currents directly under the ADC input traces

Explanation

Partitioning analog and digital ground regions keeps noisy digital return currents out of the analog reference and input network, and a single-point join near the ADC provides one defined reference potential. Digital return currents should not be routed under sensitive analog traces.