Electrical Engineering Quiz

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Questions and Answers

What is the impedance of an open circuit?

Infinite impedance (correct)

Zero impedance

Finite impedance

Variable impedance

What is the relationship between output voltage (Vout) and input voltage (Vin) in a unity-gain amplifier?

$Vout = 2Vin$

$Vout = Vin$ (correct)

$Vout = Vin + Rf$

$Vout = 1 + (Rf / R1)Vin$

What is the frequency of the signal given by Y = 3 + 2sin(4πt)?

2 Hz (correct)

1 Hz

4 Hz

8 Hz

What is a characteristic of a floating ground in an electrical circuit?

It is not electrically connected to the earth Signup and view all the answers

In a first-order system response to a step input, what percentage of the final value is achieved after one time constant?

63.2% Signup and view all the answers

Which of the following damping ratios indicates an over-damped system?

$\zeta > 1$ Signup and view all the answers

Where should a relay be connected in a circuit for safety?

On the live wire Signup and view all the answers

What is typically observed in the frequency response curve of a low-pass filter at critical frequency?

Output is half of input level Signup and view all the answers

In an inverting operational amplifier with a gain of 5, what is the ratio of the feedback resistor (Rf) to the input resistor (Rin)?

Rf/Rin = 5 Signup and view all the answers

What type of signal is characterized by discrete levels rather than a continuous range?

Digital signal Signup and view all the answers

Which of the following conditions represents high accuracy and low precision in measurements?

Varying measurement results that average close to the true value Signup and view all the answers

What does the term 'sensitivity' refer to in the context of a transducer?

The ability to detect small changes in input Signup and view all the answers

How does an oscilloscope display a signal in AC coupling mode compared to DC coupling mode?

Eliminates DC offset to show only AC variations Signup and view all the answers

In a Bode plot for a low-pass filter, what region is characterized by attenuation of the signal?

Stop band Signup and view all the answers

Which scenario represents low accuracy and high precision in measurement?

Consistently getting results that are far from the true value Signup and view all the answers

What is the formula to calculate the resistance of a wire at a given temperature?

R(T) = R0[1 + α(T - T0)] Signup and view all the answers

Which characteristic is NOT essential for an ideal transducer?

Should be sensitive to various other signals Signup and view all the answers

What is the coefficient of thermal expansion (α) of the wire given in the solved example?

$56.56 x 10^{-5} / °C$ Signup and view all the answers

What property of an ideal transducer ensures consistent and accurate measurements over time?

Reproducibility (precision) Signup and view all the answers

At what temperature is the electrical resistivity of the wire measured in the examples?

20 °C Signup and view all the answers

What is the electrical resistivity of the wire at 20.00 °C?

1.673 μΩm Signup and view all the answers

What does the term 'dynamic response' refer to in the characteristics of an ideal transducer?

Ability to respond to changes in input signals Signup and view all the answers

Which of the following is a potential consequence of a transducer inducing phase distortions?

Time lag between input and output Signup and view all the answers

Study Notes

Review Questions

Review questions were presented in the document.

Solved Example 1

Statement: Which of the following effects would most likely NOT result from routing an AC signal across an inductor?
a. a change in the frequency of the output alternating current
b. a back electromagnetic force on the input current
c. a phase lag in the output AC signal
d. a reduction in the amplitude of the AC signal
Feedback: An inductor is a linear circuit device. An AC output to an inductor will produce a linear output. Phase and amplitude change are linear effects. An inductor produces a back emf, which affects the voltage. A change in frequency in the AC signal, however, is a nonlinear process and not a function of an inductor. The correct answer is a.

Solved Example 2

Statement: A wire has a length of 1.17 m and a diameter of 5x10-5 m. The electrical resistivity, p, of the wire is 1.673 µWm at 20.00 °C and that its coefficient of thermal expansion, a, is 56.56 x10-5/°C, compute the resistance of the wire at 24.8 °C.
Feedback: The electrical resistivity of a wire at a given temperature is p = ρο[1 + α(Τ-Το)], where a is the linear coefficient of thermal expansion and the subscript zero indicates values at the reference temperature To. The resistance in the wire is related to the electrical resistivity through: R = (pL)/A = (ρL)/(π/D2/4).
Solution: R20°C = 4pL/(πD²) and R24.8°C = R20°C [1+ (56.56 × 10-5) (4.8)]. Given values are L, D, p, and α for 20°C to compute the resistance of the wire at 24.8°C.

Solved Example 3

Statement: A wire with the same material properties given in the previous problem is used as the R₁ arm of the Wheatstone bridge shown below. The Wheatstone bridge is designed to be used in deflection method mode and to act as a transducer in a system used to determine the ambient temperature in the laboratory. The length of the copper wire is fixed at 1.00 m and the diameter is 0.0500 mm. R₂ = R₃ = R₄ = 154 Ω and E₁ = 10.0 V. For a temperature of 25.8 °C, compute the output voltage, E., in volts to the nearest hundredth of a volt.
Feedback: To solve, first find the reference resistance of the wire, Ro = (ροL)/Α. Then find the new wire resistance, R, for the given ambient temperature: R = Ro[1 +α(T - To)]. Reference values are given in the previous problem. Finally, solve for the output voltage from the Wheatstone bridge: E = E[R/(R+R₂) - R₃/(R₃+R₄)].

Solved Example 4

Statement: A Wheatstone bridge has resistances R₂ = 10 Ω, R₃ = 14 Ω and R₄ = 3 Ω. Determine the value of R₁ in Ω when the bridge is used in the null method.
Feedback: In the null method, R₁/R₂ = R₃/R₄

Solved Example 5

Statement: In this RTD measurement system, what methodology classifies the use of the Wheatstone bridge?
Feedback: The resistance of an RTD changes with temperature as Ro[1+α(T-To)], where the subscript 0 indicates reference quantities at To.
Solution: 25.6 Ω

Solved Example 6

Statement: For the Wheatstone bridge shown, R₂ = R₃ = R₄ = 25 Ω and E₁ = 5 V. The maximum temperature to be sensed by the RTD is 78°C. Find the maximum output voltage from the Wheatstone bridge to the nearest thousandth volt.
Feedback: The maximum sensed temperature produces the maximum sensor resistance which yields the maximum output voltage from the bridge. Let R = R₂ = R₃ = R₄. First find the change in the RTD resistance, SR, using R = R₀α(Τ - T₀) = 0.029 Ω. Then find the output bridge voltage: E = Ei(R/(R+R₂)- R₃/(R₃+R₄)). The answer is 0.0357V, rounded off to 0.036 V.
Solution: 0.036 V

Solved Example 7

Statement: A constant gain amplifier, with gain factor G, conditions the output voltage from the Wheatstone bridge. The multimeter used to process the output voltage from the amplifier, Em, has an full-scale output of +10 V. Determine the maximum gain factor possible.
Feedback: The gain factor is determined by dividing the desired output from the amplifier by the bridge output. G = 10/E₀. This gives G = 280.11. The gain, however, must be rounded down to the nearest whole hundred because rounding up would cause the maximum voltage output to exceed the limits of the multimeter.
Solution: 200

Solved Example 8

Statement: Consider the Wheatstone bridge that is shown in Figure 4.3. Assume that the resistor R₁ is actually a thermistor whose resistance, R, varies with the temperature, T, according to the equation: R = R₀exp[-β/(T-T₀)].
Feedback: The resistivity is related to the electrical resistivity through: R = (ρL)/A = (ρL)/(π/D²/4).
Solution: (a) Eo/Ei numerical value (at 400°C), (b)Program to compute and plot, (c) Linear range, and (d) Temperature range. The resistivity of a wire is proportional to the inverse of its cross-sectional area. The normalized bridge output is almost linear at lower temperature range

Solved Example 9

Statement: A single-stage, low-pass RC filter with a resistance of 93 Ω is designed to have a cutoff frequency of 50 Hz. Determine the capacitance of the filter in units of μF.
Feedback: The cutoff frequency, fo, equals 1/(2πRC). So, C in μF equals 10⁶ x 1/(2πRfo) = 34.227 μF. Expressed with the correct number of significant figures, this is 34 μF.
Solution: 34 μF

Solved Example 10

Statement: A single-stage, passive, low-pass (RC) filter is designed to have a cutoff frequency, fc, of 100 Hz. Its resistance equals 100 Ω. Determine the filter's [a] magnitude ratio at f = 1 kHz, [b] time constant (in ms), and [c] capacitance (in μF).
Analysis: (a) M(f) = 1/√1 + (2π.fr)² and τ = 1/2πfc. So, M(f) = 1/√1+ (f/fc)² = 1/√101 = 0.0995; (b) τ = 1/2πfc = 1/(2π)(100) = 1.59 ms; (c) T = RC, so C = T/R = 15.9 μF.

Ideal Transducer Characteristics

Should be insensitive to signals other than those that should be measured
Should not alter the physical quantity being measured
Should be amenable to modifications using appropriate processing and display devices
Should have good accuracy
Should have good reproducibility (precision)
Should have amplitude linearity
Should have adequate frequency response (i.e., good dynamic response)
Should not induce phase distortions (i.e., should not induce time lag between the input and output)
Should be able to withstand hostile environments without damage
Should maintain the accuracy within acceptable limits
Should be easily available and reasonably priced

Open Circuit, Short Circuit, and Closed Circuit

Open circuit: infinite impedance
Short circuit: zero impedance
Closed circuit: finite impedance

Sketch of an Analog and Digital Signal

Analog signal: Continuous wave
Digital signal: Discrete values represented by numbers

Relay Connections

Relays are typically connected to the live wire rather than the neutral wire, safer.

Oscilloscope Display (DC and AC Coupling)

DC coupling: Displays the complete signal including the DC offset.
AC coupling: Displays only the AC component of a signal.

Output Voltage vs. Output Current (Power Supply)

In regulation: Output voltage remains constant even as the current output rises.
Out of regulation: Output voltage decreases as the current output rises.

Inverting Operational Amplifier (Gain of 5)

Gain = (Vout/Vin) = -(Rf/Rin) where Rf = R₁ and Rin = R₂
The input of the inverting amplifier is connected to R₁ while the output of the inverting amplifier is connected to R₂

Non-inverting Operational Amplifier (Gain of 3)

Gain = (Vout/Vin) = 1 + (R₂/R₁)

Voltage Follower (Unity-Gain Amplifier)

Vout = Vin
Used to isolate circuits, buffer, or increase input impedance

Analog Low-Pass RC Filter (Bode Plot)

Bandwidth: Frequency range over which signal is attenuated less than 3 dB.
Pass band: Frequency range over which signal is attenuated less than 3dB of max gain (0dB)
Critical Frequency: Frequency at which the output amplitude has fallen by −3dB of its maximum
Stop band: Frequency range where signal falls below 3dB attenuation (cut off)

Accuracy and Precision

Low accuracy, low precision: Widely scattered data, far from the target value.
Low accuracy, high precision: Data is clustered together but far from the target value.
High accuracy, low precision: Data points are grouped closely around the target value, but the distribution is wide.
High accuracy, high precision: Data points are closely grouped around the target value.

Transducer Sensitivity and Saturation

Sensitivity: rate of change of the output signal relative to the rate of change of the input signal
Saturation: When the output signal no longer increases with increases in input signal

Transducer Hysteresis

Hysteresis is the phenomenon where the output of the transducer depends on both the present value and the history of the input signal.

Dynamic System Response (First Order System)

Shows how the output changes with time after a step input in a first order system. The time constant is the time required for the system to reach approximately 63.2% of its final value.

Dynamic System Response (Second Order System)

Show the dynamic response of second order systems to a step input for varying damping ratios.

Measurement System (Transducer, Signal Conditioning, and Display Elements)

The diagram shows the pressure transducer, amplifier, filter, A/D board, and the computer, together.

Resistive Transducer

Resistive transducers measure a physical quantity (e.g., displacement, temperature, force) converted into a change in resistance.
Advantage: Relatively simple implementation, easy to use in an AC or DC circuit
Limitation: Sensitive to temperature variations

Inductive Transducer

Inductive transducers measure a physical quantity (e.g., speed or frequency) by variations in inductance.
Advantage: Good sensitivity and high range, operate with little friction
Limitation: Affected by external magnetic fields

Capacitive Transducer

Capacitive transducers measure a physical quantity by varying the capacitance.
Advantage: Low power consumption, high resolution and stability, good frequency response
Limitation: Sensitive to temperature changes, dirt/contamination affect performance

Error Analysis Examples

Various examples covering different types of errors (e.g., uncertainty in dynamic pressure, uncertainty in calculated volume).

Temperature Measurements

Different techniques (e.g., resistance temperature detectors, thermocouples, pyrometers)
Ideal conditions which provide on/off control action, sensors generates and electric output, very low drift in electric output, temperature sensing in non-intrusive, methods, and high sensitivity for very small range in temperature etc.

Pressure Measurements

Various concepts and measurement techniques (e.g., manometers, inclined manometers, dead weight testers, piezoelectric transducers.

General Questions

Various question on specific elements, such as the concept of errors (random, systematic, human), and methodologies involved in specific calculations.

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Description

Test your knowledge in electrical engineering concepts with this quiz covering topics such as impedance, amplifiers, systems response, and signal characteristics. Each question is designed to challenge your understanding of fundamental principles and practical applications in the field.