Question 1

Sinusoidal waveform properties: A single sine wave (steady-state AC) can be described as having which of the following features?

Accepted Answer

Introduction: Sine waves are fundamental to AC analysis and Fourier methods. Several equivalent descriptors apply depending on whether we look at the waveform in time, sign, or coordinate representation. This question asks you to recognize that multiple statements about a standard sine wave can simultaneously be true. Given Data / Assumptions: Ideal sinusoid with constant amplitude and frequency. Observation over one complete cycle. Standard mathematical definitions of period and quadrants. Concept / Approach: Over one cycle, the sine wave completes one period. It also has two alternations: a positive half-cycle and a negative half-cycle. In the angle (phasor) domain, we often reference four quadrants corresponding to 0–90°, 90–180°, 180–270°, and 270–360°, across which sine changes sign and magnitude systematically. Step-by-Step Solution: One period: the smallest time interval T after which the waveform repeats.Two alternations: positive and negative halves within T.Four quadrants: angle-based view spanning 360° split into four 90° sectors. Verification / Alternative check: Plot sin(θ) from 0° to 360° and note sign/magnitude behavior per quadrant; in the time domain, count zero crossings and extrema to verify two alternations within one period. Why Other Options Are Wrong: Each individual statement is correct, but the most complete answer acknowledging all is “all of the above.” Common Pitfalls: Assuming these descriptions are mutually exclusive; conflating “quadrants” (angle domain) with “alternations” (time domain). Final Answer: all of the above

Question 2

Mains frequency comparison: What is the difference in waveform period between 60 Hz utility power and 50 Hz utility power (express your choice by the closest value)?

Accepted Answer

Introduction: Time-domain understanding of mains frequency is crucial for power conversion, timing references, and alias-free sampling. The period T is the reciprocal of frequency f, so small frequency differences translate into concrete milliseconds per cycle differences. Given Data / Assumptions: f1 = 60 Hz (common in North America and parts of Asia). f2 = 50 Hz (common in Europe and many other regions). We want ΔT = |T60 − T50|. Concept / Approach: Compute T from T = 1 / f. For 60 Hz, T60 ≈ 0.01667 s = 16.67 ms. For 50 Hz, T50 = 0.020 s = 20.00 ms. The absolute difference is about 3.33 ms. Among the provided discrete choices, 3 ms is the closest approximation (rounding to the nearest millisecond). Step-by-Step Solution: T60 = 1 / 60 ≈ 0.01667 s = 16.67 ms.T50 = 1 / 50 = 0.02000 s = 20.00 ms.ΔT ≈ 20.00 − 16.67 = 3.33 ms.Closest listed value: 3 ms. Verification / Alternative check: Express ΔT precisely as 1/50 − 1/60 = (60 − 50) / (3000) s = 10/3000 s = 1/300 s ≈ 3.333 ms; rounding confirms the selected option. Why Other Options Are Wrong: 16 ms or 20 ms: These are full periods, not the difference. 4 ms: Farther from the exact 3.33 ms than 3 ms. Common Pitfalls: Mixing up frequency with period; forgetting to convert seconds to milliseconds; selecting a full period instead of the difference. Final Answer: 3 ms

Question 3

In basic electrical engineering and communications, alternating current (AC) is used for more than just lighting and motors. Broadly speaking, what are the two principal application categories for AC in modern systems?

Accepted Answer

Introduction: Alternating current (AC) underpins two enormous domains of engineering: delivering energy over distance and carrying information from one point to another. This question checks whether you can identify these two broad application categories succinctly and correctly. Given Data / Assumptions: AC refers to time-varying currents/voltages, typically sinusoidal but not limited to sine waves. We are classifying real-world uses at a high level rather than naming specific devices. Focus is on the dominant, foundational purposes served by AC in industry and communications. Concept / Approach: AC enables efficient transformation of voltage levels using transformers, which drastically reduces transmission losses. The same periodic nature of AC signals also makes them ideal carriers for modulating and transporting information in audio, radio, and data systems. Thus, the two principal categories are energy delivery (power) and signal conveyance (information). Step-by-Step Solution: 1) Identify energy role: AC is stepped up for transmission and stepped down for distribution, minimizing I^2 * R losses.2) Identify information role: AC waveforms are modulated in amplitude, frequency, or phase to encode data (audio, RF, telecom, networking).3) Map categories to choices: 'power, information' precisely names these two pillars.4) Confirm that other pairings are not standard application categories. Verification / Alternative check: Survey of utilities and telecom: electric utilities transmit AC; communications systems (audio/RF) ride on AC carriers. Both domains are ubiquitous and foundational. Why Other Options Are Wrong: direct, pulsating: describe waveform types, not application domains.electric, magnetic: name fields, not end-use categories.static, dynamic: generic physics adjectives, not application classes. Common Pitfalls: Confusing signal characteristics (e.g., pulsating) with application categories; applications are about what AC is used for, not how it looks on an oscilloscope. Final Answer: power, information

Question 4

For two sine waves of different frequencies, how does their phase difference behave over time if both continue at their respective constant frequencies?

Accepted Answer

Introduction: Phase describes the relative timing of periodic signals. When two sinusoids have different frequencies, their relative alignment does not remain fixed. This question tests conceptual understanding of phase evolution between unequal-frequency sinusoids. Given Data / Assumptions: Two ideal sine waves in steady state. Frequencies f1 and f2 are constant but not equal. No noise or modulation; purely deterministic signals. Concept / Approach: Let phases be φ1(t) = 2 * pi * f1 * t + φ1,0 and φ2(t) = 2 * pi * f2 * t + φ2,0. The phase difference Δφ(t) = φ1(t) − φ2(t) = 2 * pi * (f1 − f2) * t + (φ1,0 − φ2,0). If f1 ≠ f2, the term 2 * pi * (f1 − f2) * t grows linearly with time, making Δφ(t) change continuously. Step-by-Step Solution: 1) Write each sinusoid's instantaneous phase as 2 * pi * f * t plus a constant.2) Subtract to get the relative phase Δφ(t).3) Recognize the linear-in-time term proportional to frequency difference.4) Conclude: unequal frequencies imply a continuously changing phase difference. Verification / Alternative check: Oscilloscope Lissajous figures drift when frequencies are unequal, visibly demonstrating the evolving phase relationship as the figure slowly rotates or morphs over time. Why Other Options Are Wrong: Equal to their frequency differences: confuses rate of phase change (proportional to frequency difference) with phase itself.Difference in fixed time displacement: applies only when frequencies are the same.The same throughout time: true only for equal-frequency (and stable) sinusoids. Common Pitfalls: Mixing phase (an angle that evolves) with frequency (a rate). A small frequency mismatch causes steady, unbounded drift of phase difference. Final Answer: constantly changing

Question 5

When selecting bench test equipment for troubleshooting and characterization, a good setup should generate known stimuli and also perform which complementary function on the circuit under test?

Accepted Answer

Introduction: Effective electronic testing requires both stimulus and observation. While generators create known inputs, measurement instruments must sense what the circuit is doing in response. This question asks you to identify the complementary function to signal generation in a typical lab workflow. Given Data / Assumptions: A technician has access to common bench gear (function generator, oscilloscope, multimeter, spectrum analyzer). Goal is verification and fault isolation on a circuit under test. We seek the essential counterpart to stimulus generation. Concept / Approach: Testing is a loop: apply known signals (stimulus) and measure the resulting voltages, currents, waveforms, and spectra (sensing/observation). Without sensing, you cannot validate behavior or diagnose issues. Therefore, the complementary capability is to sense or measure circuit conditions. Step-by-Step Solution: 1) Identify stimulus tools: function generators and pattern sources.2) Identify sensing tools: oscilloscopes, DMMs, current probes, analyzers.3) Pair the two: stimulus in, observation out.4) Conclude that 'sense circuit conditions' is the correct complementary function. Verification / Alternative check: Standard troubleshooting flowcharts always include both injection and measurement steps—observe changes in node voltages/currents to localize faults. Why Other Options Are Wrong: Change circuit conditions: vague; any measurement changes loading slightly but the goal is observation, not arbitrary change.Inject signals: stimulus only; the question asks for the complementary function.Change signal frequencies: too specific and not a universal testing requirement. Common Pitfalls: Confusing tools that generate signals with those that measure them. Both are required for a closed-loop test strategy. Final Answer: sense circuit conditions

Question 6

An oscilloscope shows a sinusoidal signal with a peak excursion of 3 major divisions above the zero reference. If the vertical sensitivity is 5 V/cm (5 volts per major division), what is the RMS value of the AC voltage?

Accepted Answer

Introduction: Relating oscilloscope deflection to RMS voltage requires converting displayed amplitude (in divisions) to volts and then applying the sinusoidal peak-to-RMS relationship. This problem ensures comfort with scope scaling and AC amplitude definitions. Given Data / Assumptions: Peak height above zero: 3 major divisions. Vertical scale: 5 V per division. Signal is a pure sine wave; use the standard RMS relation. Concept / Approach: Convert divisions to peak voltage: Vp = divisions * volts_per_div. For a sine wave, Vrms = Vp / sqrt(2). Do not confuse peak (0-to-maximum) with peak-to-peak (maximum-to-minimum). Here the statement explicitly refers to peak above zero, so Vp is used directly. Step-by-Step Solution: 1) Compute peak: Vp = 3 * 5 V = 15 V.2) Use sine relation: Vrms = Vp / sqrt(2).3) Evaluate: Vrms ≈ 15 / 1.414 ≈ 10.606 V.4) Round sensibly to one decimal: ≈ 10.6 V. Verification / Alternative check: If the display had been 3 divisions peak-to-peak, Vpp = 15 V and Vrms would differ (Vpp / 2√2). But the problem says 'peak' above zero, confirming the calculation used. Why Other Options Are Wrong: 5.3 V: corresponds to using half the correct peak or mis-scaling.15.0 V: that is peak, not RMS.21.2 V: would be Vpp for 3 divisions at 5 V/div, not applicable here. Common Pitfalls: Confusing peak with peak-to-peak, or forgetting that RMS for a pure sine is Vp / sqrt(2), not Vp / 2. Final Answer: 10.6 V

Question 7

When the goal is to compare two signals simultaneously (for example, input versus output of an amplifier) and see timing and amplitude relationships on the same screen, which piece of test equipment makes this task easiest?

Accepted Answer

Introduction: Visual comparison of two waveforms is central to debugging amplifiers, filters, and digital interfaces. The right tool should display both signals with a common time base so that relative phase, delay, gain, and distortion are immediately visible. Given Data / Assumptions: Two signals need to be observed at once. We care about amplitude and time alignment. Real-time visualization is preferred. Concept / Approach: A dual trace (two-channel) oscilloscope shows both signals on the same screen with a synchronized horizontal sweep. You can overlay or stack channels, measure time differences, and quantify gains/offsets. Other instruments either cannot show two time-domain traces together or do not provide time correlation directly. Step-by-Step Solution: 1) Determine requirement: simultaneous, time-correlated display of two signals.2) Match instrument capability: two-channel scope provides exactly that.3) Confirm ancillary features: cursors, math, and triggering further aid comparison.4) Choose dual trace oscilloscope as the most straightforward option. Verification / Alternative check: Modern DSOs (digital storage oscilloscopes) with two channels are standard in labs for exactly this purpose; engineers routinely compare input and output or two nodes in a circuit. Why Other Options Are Wrong: Spectrum analyzer: frequency-domain instrument; not suited to time-domain comparison.Multimeter: single scalar readings; no waveforms.Function generator: produces signals; does not display two signals for comparison. Common Pitfalls: Trying to infer timing relationships from separate single-channel captures; simultaneity is critical for accurate comparison. Final Answer: dual trace oscilloscope

Question 8

A current waveform varies periodically from zero up to a positive maximum, returns to zero, and repeats without reversing polarity. What is the correct classification of this signal?

Accepted Answer

Introduction: Waveform terminology distinguishes DC, AC, and intermediate cases that are neither constant nor sign-reversing. Correct classification helps predict effects such as rectification outcomes and filter behavior. Given Data / Assumptions: Current is always nonnegative (never below zero). It starts at zero, rises to a positive maximum, returns to zero, and repeats. The pattern is periodic. Concept / Approach: An alternating signal must change polarity (positive to negative and back). A direct signal is constant over time. The described waveform is periodic and unidirectional, which is the definition of a pulsating (or pulsating DC) signal often seen after rectification before filtering. Step-by-Step Solution: 1) Check polarity: waveform never goes negative → not alternating.2) Check constancy: amplitude varies over time → not direct (not constant DC).3) Check periodicity: repeats → qualifies as pulsating.4) Conclude: the correct classification is pulsating. Verification / Alternative check: Half-wave or full-wave rectifier outputs are classic examples of pulsating DC: unidirectional but time-varying and periodic. Why Other Options Are Wrong: Direct: implies constant magnitude; contradicted by variation.Alternating: requires polarity reversal; not present.Repetitive: true but too generic; does not specify unidirectional variation. Common Pitfalls: Assuming any periodic waveform is alternating. Alternating specifically means sign reversal, not merely repetition. Final Answer: pulsating

Question 9

Why do electric utility companies distribute alternating current (AC) rather than direct current (DC) for most public power grids?

Accepted Answer

Introduction: The choice of AC for public grids dates to the 'war of currents' and persists for practical engineering reasons. Understanding why AC dominates clarifies design decisions in generation, transmission, and distribution. Given Data / Assumptions: Focus on large-scale transmission and distribution. Historical and technical context: transformers and line losses. Safety and application considerations are secondary to efficiency. Concept / Approach: Long-distance transmission favors high voltage and low current to reduce I^2 * R losses. AC voltages are easily stepped up or down with transformers, enabling efficient high-voltage transmission and safe local distribution. Although modern HVDC exists for specific corridors, AC remains the default due to transformer simplicity and network interconnectivity. Step-by-Step Solution: 1) Goal: minimize power loss P_loss = I^2 * R over long lines.2) Strategy: increase transmission voltage to reduce current for given power.3) Enabler: transformers efficiently change AC voltage levels.4) Outcome: AC systems provide flexible, economical transmission and distribution. Verification / Alternative check: Compare AC transformer simplicity to DC conversion historically; until modern power electronics matured, DC voltage conversion was inefficient, cementing AC as the standard. AC grids also synchronize many generators, aiding reliability. Why Other Options Are Wrong: No longer a need for DC: false; DC is widely used in electronics and specific transmission links.DC is more dangerous: safety depends on many factors; not the key reason.Not enough batteries: irrelevant to bulk generation and grid design. Common Pitfalls: Overgeneralizing HVDC's niche advantages (long undersea links, asynchronous ties) as reasons to prefer DC everywhere; grid reality is more nuanced. Final Answer: it is easier to transmit ac

Question 10

A sine wave has an amplitude of 100 mV peak-to-peak (Vpp). What RMS voltage would a typical true-RMS voltmeter read for this signal?

Accepted Answer

Introduction: Converting between peak-to-peak, peak, and RMS values is a standard AC measurement task. A correct conversion prevents order-of-magnitude mistakes when reading or specifying instrumentation levels. Given Data / Assumptions: Sine wave with Vpp = 100 mV. We seek the RMS value as a voltmeter would report. True-RMS behavior assumed for sinusoidal input. Concept / Approach: For a sine wave: Vpp = 2 * Vp and Vrms = Vp / sqrt(2). Combining, Vrms = Vpp / (2 * sqrt(2)). This formula directly converts peak-to-peak to RMS for sinusoids. Step-by-Step Solution: 1) Compute peak: Vp = Vpp / 2 = 100 mV / 2 = 50 mV.2) Convert to RMS: Vrms = Vp / sqrt(2) = 50 mV / 1.414 ≈ 35.36 mV.3) Round appropriately: ≈ 35.4 mV.4) Select the matching option. Verification / Alternative check: Use the combined formula: Vrms = 100 mV / (2 * 1.414) = 100 / 2.828 ≈ 35.36 mV, consistent with the step-by-step result. Why Other Options Are Wrong: 14.14 mV: equals 10 mV * sqrt(2); not related to 100 mVpp.63.7 mV and 70.7 mV: correspond to RMS values for much larger peaks; numerically inconsistent with 100 mVpp. Common Pitfalls: Using Vpp / 2 as RMS or forgetting the sqrt(2) factor; both errors overstate the RMS value by 1.414×. Final Answer: 35.4 mV

Question 11

On an oscilloscope, which control is used to scale the vertical axis so that the graticule's major/minor divisions can be read directly as a signal's amplitude?

Accepted Answer

Introduction: Reading amplitude on an oscilloscope requires the correct vertical scale. Knowing which control sets that scale is essential for accurate, repeatable measurements in the lab or field. Given Data / Assumptions: A standard analog or digital scope with graticule. Vertical sensitivity adjustable in steps (e.g., 1 V/div, 2 V/div, 5 V/div). We want to convert divisions to volts directly. Concept / Approach: The volts-per-division (volts/cm) control sets how many volts correspond to one major vertical division. Multiplying the observed number of divisions by this setting yields the signal amplitude. Other controls do not change the scale in volts per division. Step-by-Step Solution: 1) Choose a volts/div setting that fits the waveform on screen.2) Count the divisions from zero reference to peak.3) Multiply by volts/div to get peak voltage; apply conversion to RMS if needed.4) Record or compare as required. Verification / Alternative check: Scopes often display the current volts/div setting on-screen; changing it rescales the vertical axis immediately—confirming that this control governs amplitude scaling. Why Other Options Are Wrong: Time/cm control: sets horizontal time base, not amplitude scale.Position control: shifts the trace vertically; does not change scaling.Intensity control: adjusts brightness only. Common Pitfalls: Failing to note the volts/div applied to each channel, leading to misread amplitudes when comparing traces. Final Answer: volts/cm control

Question 12

Which instrument is specifically designed to directly measure the frequency of a periodic waveform with high accuracy and display it as a numerical value?

Accepted Answer

Introduction: While many instruments can imply frequency, only certain devices are optimized to measure and display it numerically with precision. This question distinguishes between general-purpose tools and dedicated frequency-measurement instruments. Given Data / Assumptions: Periodic input signal of unknown frequency. Desire for direct numerical readout. Standard lab instruments available. Concept / Approach: A frequency meter/counter counts cycles or zero-crossings over a gate time, computes frequency f = counts / gate_time, and displays the result. Oscilloscopes can estimate frequency by measuring period from the trace, but that method is less precise and more user-dependent. Signal generators produce signals; they are not measurement devices for unknown signals. Step-by-Step Solution: 1) Feed the unknown periodic signal into the counter's input with proper conditioning.2) The counter uses a stable timebase (crystal oscillator) to define gate intervals.3) It tallies cycles within the gate and computes the frequency in Hz.4) The display shows a direct numeric frequency readout. Verification / Alternative check: Comparing the counter's readout with an oscilloscope timebase measurement typically shows the counter's higher precision and stability, especially for high or very low frequencies. Why Other Options Are Wrong: Oscilloscope: visual tool; frequency is inferred, not directly measured numerically (unless the scope has a built-in counter function).Audio/RF generators: sources, not measurement devices. Common Pitfalls: Relying solely on scope graticule for precision measurements where a counter would be more accurate. Final Answer: frequency meter or counter

Question 13

In electronics test and measurement, which single instrument is specifically designed to generate multiple standard waveforms—such as square, triangular, and sawtooth—over a selectable frequency and amplitude range?

Accepted Answer

Introduction: A modern laboratory often needs a versatile source capable of producing different periodic waveforms for testing filters, amplifiers, and digital circuits. This question checks recognition of the instrument purpose-built to create common waveforms like sine, square, triangle, and sawtooth with controllable parameters. Given Data / Assumptions: We need one instrument that outputs multiple waveform shapes. Output frequency, amplitude, and duty cycle (for square) are typically adjustable. Use cases include sweeping circuits under test and stimulating time-domain responses. Concept / Approach: A function generator is designed to synthesize several standard functions (waveforms). It commonly provides sine, square, triangle, ramp/sawtooth, and often pulse outputs. Controls typically include frequency, amplitude, DC offset, and duty cycle, making it the correct tool for general-purpose waveform creation. Step-by-Step Solution: 1) Identify the requirement: multiple waveform shapes (square, triangular, sawtooth).2) Map to instruments: RF generators focus on sine at RF bands; AF generators focus on audio-band sine.3) Frequency meters/counters measure frequency; they do not generate waveforms.4) Only a function generator natively produces the requested set of waveforms. Verification / Alternative check: Check front panels of typical bench function generators: waveform-select buttons (sine, square, triangle, ramp), plus knobs/keys for frequency and amplitude, confirm suitability for the stated need. Why Other Options Are Wrong: Radio frequency generator: primarily sine at RF; not multi-waveform by default. Audio frequency generator: primarily sine in the audio band. Frequency meter/counter: measures frequency; no output generation. Pulse height analyzer: analyzes pulses; does not generate standard periodic waveforms. Common Pitfalls: Assuming any “signal generator” provides all shapes. Many specialize in sine-only outputs; always verify waveform capability. Final Answer: a function generator

Question 14

In basic wave and communication theory, the distance a signal’s energy travels during one complete cycle is called the signal’s _________. Select the correct term.

Accepted Answer

Introduction: To analyze electromagnetic and acoustic waves, it is essential to distinguish time-domain and spatial-domain properties. The question targets the spatial measure associated with a single cycle of oscillation, a cornerstone concept in RF, optics, and acoustics. Given Data / Assumptions: Uniform medium with constant propagation speed v. Periodic waveform with frequency f and period T = 1 / f. Standard terminology used in physics and communications. Concept / Approach: Wavelength (lambda) is defined as the physical distance a wave travels in one period. It relates to speed and frequency via lambda = v / f. Do not confuse wavelength with period (time per cycle), frequency (cycles per second), or amplitude (maximum displacement or field strength). Step-by-Step Solution: 1) Recognize the question asks for a distance per cycle (spatial measure).2) Identify correct term: wavelength is distance traveled in one cycle.3) Use relationship if needed: lambda = v / f ensures units of meters.4) Conclude that the appropriate term is “wavelength”. Verification / Alternative check: Example: In free space, v ≈ 3 * 10^8 m/s. For f = 100 MHz, lambda = 3 m, which matches widely taught VHF antenna dimensions. Why Other Options Are Wrong: Amplitude: magnitude of oscillation, not a distance per cycle. Frequency: cycles per second; temporal rate, not a spatial length. Period: time for one cycle, not a distance. Phase lead: a relative angle shift, not a spatial measure. Common Pitfalls: Interchanging period and wavelength because both describe “one cycle.” Always check units (seconds vs meters). Final Answer: wavelength

Question 15

Why is alternating-current (AC) power transmission more effective than direct-current (DC) transmission over long distances in conventional grids?

Accepted Answer

Introduction: Power loss during transmission is predominantly resistive, scaling with the square of current. This question tests understanding of why legacy AC grids efficiently move power over long distances using transformers. Given Data / Assumptions: Line resistance causes heating losses approximately equal to I^2 * R. Transformers operate on AC and allow voltage conversion with high efficiency. Total transmitted power P ≈ V * I (ignoring reactive effects for simplicity). Concept / Approach: For a given power P, increasing transmission voltage V allows current I = P / V to decrease. Since resistive loss is I^2 * R, raising V and lowering I dramatically reduces losses. AC enables practical use of transformers for stepping voltage up (transmission) and down (distribution), which is the traditional reason for AC's advantage. Step-by-Step Solution: 1) Start with P = V * I for the same required delivered power.2) Increase V via a step-up transformer so I = P / V becomes small.3) Line loss reduces as I^2 * R; with smaller I, losses drop quadratically.4) Near loads, use step-down transformers to safely reduce V and raise I as needed. Verification / Alternative check: Compare two scenarios moving 100 MW: at 100 kV the current is 1,000 A; at 500 kV it is 200 A. Loss ratio scales roughly as (200/1000)^2 = 1/25—showing the dramatic reduction. Why Other Options Are Wrong: Height of power lines: affects clearance and safety, not fundamental efficiency. Use of AC generators: a historical fact but not the efficiency reason. Very high voltages: true but incomplete—transformers (enabled by AC) make this practical and safe; option (c) states the mechanism. Zero resistance: incorrect; lines have finite resistance. Common Pitfalls: Confusing the outcome (high voltage) with the enabling mechanism (transformers on AC). Modern HVDC also achieves low loss but uses power electronics; the question targets the classical AC advantage. Final Answer: due to step-up and step-down transformers reducing I^2R losses

Question 16

A rectangular waveform with a duty cycle of exactly 50% (equal high and low times within each period) is more specifically referred to as a:

Accepted Answer

Introduction: Different periodic waveforms are classified by shape and timing metrics. Duty cycle is a key descriptor for rectangular waveforms. This question verifies that a 50% duty cycle rectangular wave is called a square wave. Given Data / Assumptions: Rectangular waveform with equal high and low durations. Ideal edges and fixed period T. Symmetry about the mid-level. Concept / Approach: Rectangular waves become square waves when the duty cycle equals 50%, meaning the signal is high for T/2 and low for T/2 each period. Sawtooth and triangle waves vary linearly between levels; they are not rectangular. An impulse train consists of narrow pulses with low duty cycle, not 50% rectangular. Step-by-Step Solution: 1) Identify waveform family: rectangular.2) Check duty cycle: D = 50% → high time equals low time.3) By definition, a 50% rectangular wave is a square wave.4) Conclude with the specific term “square wave”. Verification / Alternative check: Fourier series symmetry: a square wave contains only odd harmonics with 1/n amplitude, consistent with equal high/low symmetry; non-50% rectangular waves exhibit even harmonic content as well. Why Other Options Are Wrong: C wave: not a standard term. Sawtooth: linear rise with sharp fall (or vice versa), not rectangular. Triangle: symmetrical linear rise and fall, not flat tops/bottoms. Impulse train: consists of very brief pulses, not 50% duty. Common Pitfalls: Assuming any rectangular wave is a square wave; 50% duty is the defining condition. Final Answer: square wave

Question 17

A signal has a measured period of 10 microseconds (10 µs). Using f = 1 / T, determine the frequency of this signal in hertz and select the closest option.

Accepted Answer

Introduction: Period and frequency are reciprocals. Converting one to the other is a basic skill used across oscilloscopes, counters, and communication systems. Here we compute frequency from a given period in microseconds. Given Data / Assumptions: Period T = 10 µs = 10 * 10^-6 s. Ideal periodic signal; measurement errors ignored. Use the reciprocal relation f = 1 / T. Concept / Approach: Compute f by taking the inverse of T and then convert to a convenient metric prefix. With microseconds, expect frequency in the tens or hundreds of kilohertz range. Step-by-Step Solution: 1) Express T in seconds: T = 10 × 10^-6 s = 1 × 10^-5 s.2) Apply f = 1 / T: f = 1 / (1 × 10^-5) = 1 × 10^5 Hz.3) Convert to kHz: 1 × 10^5 Hz = 100 kHz.4) Select the closest option: 100 kHz. Verification / Alternative check: Sanity check: A 10 µs period implies 100,000 cycles per second; this aligns with typical PWM and microcontroller timing domains. Why Other Options Are Wrong: 100 Hz and 1000 Hz: correspond to millisecond-level periods, not microseconds. 10 kHz: corresponds to T ≈ 100 µs, ten times larger than given. 1 MHz: corresponds to T = 1 µs, ten times smaller than given. Common Pitfalls: Forgetting to convert microseconds to seconds or mishandling powers of ten. Final Answer: 100 kHz

Question 18

On an oscilloscope, which control should you adjust to display more cycles of a periodic signal across the screen without changing the signal itself?

Accepted Answer

Introduction: Oscilloscopes display signals versus time. To see more cycles, you must compress the waveform horizontally (increase the time span shown) rather than alter amplitude or position. This question tests familiarity with core scope controls. Given Data / Assumptions: A stable, periodic input signal. Standard bench oscilloscope with time/div (time per division) and volts/div controls. Goal: show more cycles on the same screen width. Concept / Approach: The time/div (or time/cm) control sets the horizontal scale. Increasing this value means each division represents more time, so the total time across the graticule increases, revealing more cycles within the same width. Step-by-Step Solution: 1) Identify desired outcome: more periods visible horizontally.2) Adjust time/div upward (e.g., from 0.5 ms/div to 2 ms/div).3) Observe more cycles fit across the ten divisions of the screen.4) Leave volts/div and positions unchanged; they affect vertical scale and offset, not cycles displayed. Verification / Alternative check: If time/div is doubled, the displayed time window doubles, and roughly twice as many cycles appear (for a constant-frequency signal). Why Other Options Are Wrong: Horizontal/vertical position: shifts the trace; does not change scale. Volts/cm: changes amplitude scale, not the number of cycles. Trigger slope: affects triggering edge, not horizontal time scale. Common Pitfalls: Turning the volts/div knob when the goal is temporal scaling, or misinterpreting “higher setting” as faster sweep instead of greater time per division. Here “higher time/cm” means a larger time value per division. Final Answer: time/cm to a higher setting

Question 19

An ammeter reads 20 mA for a sinusoidal AC current (assume the meter indicates RMS). What is the corresponding peak-to-peak current of this sine wave?

Accepted Answer

Introduction: Many meters report RMS values, but design and analysis often require peak or peak-to-peak amplitudes. Converting between RMS and peak values for a pure sine wave is a common task in AC analysis. Given Data / Assumptions: Measured current Irms = 20 mA. Waveform is a pure sinusoid. Relationship for sine: Ipeak = Irms * sqrt(2), Ipp = 2 * Ipeak. Concept / Approach: For sinusoidal signals, RMS and peak quantities are linked by sqrt(2). Once peak is found, peak-to-peak is simply twice the peak. This stems from the trigonometric RMS of sinusoids over a full cycle. Step-by-Step Solution: 1) Compute Ipeak = Irms * sqrt(2) = 20 mA * 1.414 ≈ 28.28 mA.2) Compute Ipp = 2 * Ipeak ≈ 2 * 28.28 mA ≈ 56.57 mA.3) Round to the nearest option: approximately 57 mA.4) Report Ipp ≈ 57 mA. Verification / Alternative check: Reverse-check: If Ipp ≈ 57 mA, then Ipeak ≈ 28.5 mA and Irms ≈ 28.5 / 1.414 ≈ 20.1 mA, consistent with the given meter reading. Why Other Options Are Wrong: 14 mA and 28 mA: correspond to peak or RMS misinterpretations, not peak-to-peak. 40 mA: equals 2 * Irms, but peak-to-peak requires 2 * Ipeak. 63 mA: would imply Irms ≈ 22.3 mA; not consistent with 20 mA reading. Common Pitfalls: Confusing peak with peak-to-peak, or forgetting the sqrt(2) factor for sinusoids. Final Answer: 57 mA

Question 20

A voltmeter reads a sinusoidal AC signal as 500 mV (assume the meter reports RMS). What is the average value of the corresponding full-wave–rectified sine wave?

Accepted Answer

Introduction: Different “measures” of a sine wave—RMS, peak, and average (of the rectified waveform)—serve different purposes. This problem asks for the mean of the absolute value (full-wave–rectified average) given an RMS reading. Given Data / Assumptions: Measured Vrms = 500 mV for a pure sinusoid. Relationships: Vpeak = Vrms * sqrt(2); Vavg(rectified) = (2 / π) * Vpeak ≈ 0.637 * Vpeak. We are not asking the algebraic average over one full cycle (which is zero). Concept / Approach: Convert the RMS value to peak, then apply the rectified-average factor. This is standard in AC measurement theory and is foundational for interpreting “average responding” meters calibrated to RMS for sinusoidal inputs. Step-by-Step Solution: 1) Compute Vpeak = 0.5 V * 1.414 ≈ 0.7071 V.2) Compute Vavg(rectified) = 0.637 * Vpeak ≈ 0.637 * 0.7071 ≈ 0.4509 V.3) Convert to millivolts: ≈ 451 mV.4) Choose the closest option: 451.0 mV. Verification / Alternative check: Using exact factors: (2/π) * sqrt(2) ≈ 0.9003; 0.9003 * 500 mV ≈ 450.2 mV, matching the rounded result. Why Other Options Are Wrong: 159.0 mV and 318.5 mV: mismatch common factors; do not follow the correct sequence. 353.5 mV: equals Vrms * 0.707; not the rectified-average relation. 500.0 mV: equals Vrms; not the rectified average. Common Pitfalls: Confusing average of the actual sinusoid (zero) with average of its rectified magnitude, or skipping the conversion from RMS to peak before applying the 0.637 factor. Final Answer: 451.0 mV

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