Question 1

For improving the quality factor (Q) of a radio‐frequency coil (inductor), which choice of wire geometry is best: long, thin, thick, or long and thin? Explain considering Q = ωL / R and copper loss minimization.

Accepted Answer

Introduction / Context: In electrical and electronics engineering, the quality factor Q of a coil indicates how efficiently it stores magnetic energy relative to resistive losses. A higher Q means lower copper loss and sharper resonance in tuned circuits. This question asks how the choice of wire affects Q when the inductance value is fixed by design. Given Data / Assumptions: Quality factor: Q = ωL / R for a coil at angular frequency ω. Inductance L is set by turns, core/geometric form, and coil dimensions. Resistance R depends on wire length, cross-sectional area, temperature, and frequency (skin effect at RF). Concept / Approach: To increase Q at a given frequency and inductance, we must reduce the series resistance R. For a given resistivity ρ and length ℓ, R = ρℓ / A, where A is the conductor's cross-sectional area. A thicker wire increases A, which reduces R and thereby increases Q. A longer wire increases ℓ, which increases R and lowers Q. At radio frequencies, skin depth reduces the effective cross-section, further favoring thicker or Litz wire to keep R small. Step-by-Step Solution: Write Q = ωL / R; maximize Q by minimizing R for the chosen L.Use R = ρℓ / A; increasing A (thicker wire) decreases R.Avoid unnecessary length; longer wire increases R and lowers Q. Verification / Alternative check: Compare two coils with identical L: the coil wound with thicker wire exhibits lower DC and AC (skin-effect) resistance and hence higher measured Q. Why Other Options Are Wrong: 'long' increases resistance and reduces Q.'thin' increases resistance by reducing area.'long and thin' is the worst combination for Q.'short and thick' would be ideal, but the option provided as correct among the listed choices is 'thick' (shortness is implied by good winding practice). Common Pitfalls: Ignoring skin effect; assuming inductance alone sets Q without considering loss. Final Answer: thick

Question 2

On a CRO (oscilloscope), a Lissajous figure appears as a straight line at 45° to the x-axis. If the X-plate is driven by x(t) = 2 sin(ωt), what Y-plate input y(t) produces this pattern?

Accepted Answer

Introduction / Context: Lissajous figures on a CRO result from applying sinusoidal voltages to the horizontal (X) and vertical (Y) plates. The observed shape encodes the relative amplitude, frequency, and phase between the two signals, which is a classic laboratory method to compare frequencies and phases. Given Data / Assumptions: X input: x(t) = 2 sin(ωt). Observed figure: straight line at 45° to the x-axis. Same frequency applied to both axes (standard Lissajous measurement for phase). Concept / Approach: A straight line indicates zero phase difference or 180° phase difference with amplitude ratios defining slope. A 45° line with positive slope requires equal amplitudes and zero relative phase (or both inverted together). Therefore, the Y-input must match the X-input in both amplitude and phase: y(t) = 2 sin(ωt). Any phase shift would rotate or thicken the line into an ellipse, and an amplitude difference would change the slope away from 45°. Step-by-Step Solution: Desired slope = +1 ⇒ |Y|/|X| = 1.Straight line (not ellipse) ⇒ phase difference Δφ = 0° (or 180° for negative slope).Hence y(t) = 2 sin(ωt) gives a +45° line. Verification / Alternative check: Plot x = 2 sin θ, y = 2 sin θ ⇒ y = x, a 45° line. Why Other Options Are Wrong: ±45° phase shifts produce an ellipse, not a perfect line; amplitude squaring (2^2) is dimensionally incorrect here. Common Pitfalls: Confusing slope sign with phase sign; forgetting equal amplitudes are required for 45°. Final Answer: 2 sin ωt

Question 3

For a mica capacitor used in measurement and RF work, the dielectric loss angle δ is typically closest to which value?

Accepted Answer

Introduction / Context: The loss angle δ (and dissipation factor tan δ) describe dielectric losses in capacitors. Low-loss dielectrics are preferred for precision and RF applications to minimize heating and phase error. Mica is a classic low-loss dielectric widely used in high-stability circuits. Given Data / Assumptions: Mica capacitors are low-loss with very small tan δ. We seek an order-of-magnitude choice for the loss angle in degrees. Concept / Approach: For a high-quality dielectric, tan δ is small (often 10^-3 to 10^-4 region for mica, depending on frequency and construction). A small tan δ corresponds to a small δ in radians and hence in degrees. Among the provided options, 1° best reflects a very small angle, whereas 5°, 15°, or 25° would imply unacceptably high loss for precision mica capacitors. Step-by-Step Solution: Recognize that δ is small for mica; values significantly larger than a degree would not be termed ”low-loss”.Choose the smallest practical option offered consistent with typical datasheets: ~1°. Verification / Alternative check: Industrial mica parts commonly specify dissipation factors below 0.001–0.003 at 1 kHz; converting to angles gives roughly sub-degree. Why Other Options Are Wrong: 5°, 15°, or 25° would correspond to high loss (large tan δ), not typical of mica. Common Pitfalls: Assuming all capacitor types share similar loss; electrolytics and paper types are far lossier than mica. Final Answer: 1°

Question 4

A thermocouple-type AC voltmeter indicates which electrical quantity of an applied waveform when properly calibrated?

Accepted Answer

Introduction / Context: Thermocouple voltmeters convert electrical energy into heat and then into a temperature-dependent electrical signal. Because heating depends on the mean of the square of the current (or voltage across a fixed resistance), these instruments naturally respond to the root-mean-square (rms) quantity, making them valuable for non-sinusoidal waveforms as true-RMS sensors. Given Data / Assumptions: Thermocouple sensor measures temperature rise due to Joule heating in a heater element. Heating power P ∝ I^2R or V^2/R averaged over time. Instrument is calibrated in rms volts for a sinusoidal reference and reads true-RMS for arbitrary waveforms within bandwidth. Concept / Approach: Since the sensor integrates power over time, its output is proportional to the average of v^2(t). The voltage equivalent is V_rms = sqrt( average{ v^2(t) } ). Therefore, the proper reading is rms value. Peak, average (rectified), or peak-to-peak indications correspond to other measurement principles (diode rectifier, crest detector, or oscilloscope, respectively). Step-by-Step Solution: Heating element: P(t) = v^2(t)/R; the thermocouple responds to ⟨P⟩.Thus meter scale is proportional to sqrt(⟨v^2(t)⟩) = V_rms. Verification / Alternative check: Check on a sine: V_rms = V_max/√2; instrument agrees with standard definitions. Why Other Options Are Wrong: Peak or peak-to-peak require different detection; average rectified is used in simple diode meters, not thermocouple. Common Pitfalls: Assuming ”average” equals ”rms” for all waveforms; true only for specific shapes with scale factors. Final Answer: rms value

Question 5

Two-wattmeter method for three-phase power: identify the correct statement relating wattmeter readings and power factor in a 3-wire system (balanced or unbalanced loads).

Accepted Answer

Introduction / Context: The two-wattmeter method is a standard technique for measuring total three-phase power in 3-wire systems. It works for both star and delta connections. Relationships between wattmeter readings and load power factor are well-known and provide diagnostic insight into system conditions. Given Data / Assumptions: Three-phase, 3-wire system; method applies to star or delta loads. Wattmeter readings: W1 = V_L I_L cos(30° + φ), W2 = V_L I_L cos(30° − φ) for a balanced load with displacement angle φ. Total power P = W1 + W2. Concept / Approach: At unity power factor (φ = 0°), W1 = W2 = V_L I_L cos 30° (both positive and equal). At φ = 60° (power factor 0.5), one reading becomes zero: cos(30° + 60°) = cos 90° = 0. At φ = 90° (purely reactive; power factor zero), readings are equal in magnitude and opposite in sign because cos(120°) = −cos(60°) = −0.5 and cos(−60°) = 0.5. Hence the only correct statement among the choices is that equal and opposite readings indicate pf = 0. Step-by-Step Solution: Unity pf: φ = 0° ⇒ W1 = W2 > 0 (not zero).pf = 0.5: φ = 60° ⇒ one wattmeter = 0.pf = 0: φ = 90° ⇒ W1 = −W2. Verification / Alternative check: Sum P = W1 + W2 gives zero when readings are equal and opposite, matching reactive load with zero real power. Why Other Options Are Wrong: Method is not limited to star loads; and equal readings do not imply pf = 0.5; at pf = 1 no wattmeter reads zero. Common Pitfalls: Mixing the φ = 60° condition (one zero reading) with φ = 0° (equal positive readings). Final Answer: When the two wattmeters read equal and opposite values, the power factor is zero

Question 6

In a cathode-ray oscilloscope (CRO), which of the following is not part of the electron gun assembly?

Accepted Answer

Introduction / Context: A CRO creates and steers an electron beam to draw traces on the phosphor screen. The electron gun forms and accelerates the beam, the deflection system steers it, and the screen converts kinetic energy into visible light. Knowing which components belong to which subsystem is fundamental for instrumentation. Given Data / Assumptions: Electron gun functions: emission, acceleration, beam shaping/focusing, intensity control. Deflection system: electrostatic plates that steer the beam horizontally (X) and vertically (Y). Concept / Approach: The electron gun includes a heated cathode, a control grid for beam current (intensity), and a series of anodes for acceleration and electrostatic focusing. The X–Y plates are physically downstream of the gun and provide deflection fields; they are not part of the beam-forming gun itself. Step-by-Step Solution: List gun components: cathode, grid, focusing and accelerating anodes.Identify deflection system: separate pair(s) of plates unrelated to emission/acceleration.Therefore, X–Y plates are not a gun component. Verification / Alternative check: Block diagram and cutaway views of CROs clearly show distinct ”gun” and ”deflection” sections. Why Other Options Are Wrong: Cathode, grid, and anodes are core elements of the electron gun. Common Pitfalls: Assuming anything inside the tube neck is the gun; the deflection plates are separate functional elements. Final Answer: X–Y deflection plates

Question 7

A moving-iron voltmeter has coil resistance 500 Ω and inductance 1 H. It reads 250 V on 250 V DC. With an added 2000 Ω series resistor, what will it read on 250 V, 50 Hz AC? (Assume the scale is effectively linear over this range.)

Accepted Answer

Introduction / Context: Moving-iron (MI) voltmeters are commonly used on AC and DC. Their coil has resistance and inductance, so at AC the impedance magnitude is greater than the DC resistance, leading to a slightly smaller current for the same applied RMS voltage. If the instrument scale is set by a DC calibration point, the AC reading can shift because the deflection depends on current (approximately linear in this operating region per the problem statement). Given Data / Assumptions: Coil: R_coil = 500 Ω, L = 1 H. Series resistor: R_s = 2000 Ω. DC calibration: 250 V produces full-scale indication (i.e., I_DC = 250 / (R_coil + R_s) = 250 / 2500 = 0.1 A). AC test: 250 V, f = 50 Hz; assume effective linearity of indication with coil current near this point. Concept / Approach: For AC, total impedance Z = √(R_total^2 + (ωL)^2), where R_total = R_coil + R_s and ω = 2πf. Compute AC current I_AC = V / |Z|. With the problem's linear-scale assumption, indicated voltage ≈ 250 * (I_AC / I_DC). Step-by-Step Solution: R_total = 500 + 2000 = 2500 Ω.ω = 2π * 50 ≈ 314.16 rad/s; X_L = ωL ≈ 314.16 Ω.|Z| = √(2500^2 + 314.16^2) ≈ 2519.66 Ω.I_AC = 250 / 2519.66 ≈ 0.0992 A; I_DC = 0.1 A.Indicated ≈ 250 * (0.0992 / 0.1) ≈ 248 V. Verification / Alternative check: The small increase in impedance from inductive reactance slightly lowers current and reading compared with DC. Why Other Options Are Wrong: Values above 250 V contradict the increased impedance at AC; 252 V or 260 V are not plausible; 250 V ignores reactance. Common Pitfalls: Forgetting series resistance; using R instead of |Z| at AC; assuming MI response is strictly I^2 when the problem directs a linear assumption near calibration. Final Answer: 248 V

Question 8

A ballistic galvanometer shows a first swing of 25° when a charge of 100 μC passes through it. What charge is required for a first swing of 50° (assume proportionality of first swing to total charge)?

Accepted Answer

Introduction / Context: A ballistic galvanometer is designed to measure total charge passed in a short pulse. Its initial deflection (first swing) is proportional to the impulse of current and hence to the total charge, provided damping is small and the pulse duration is short compared with the galvanometer period. This is a standard proportional-scaling question. Given Data / Assumptions: First swing θ ∝ Q (total charge). Case 1: Q1 = 100 μC → θ1 = 25°. Case 2: Q2 → θ2 = 50°. Same instrument settings and conditions; damping unchanged. Concept / Approach: Since θ ∝ Q, the ratio of deflections equals the ratio of charges. Doubling the first swing from 25° to 50° requires doubling the charge through the galvanometer. Step-by-Step Solution: θ2 / θ1 = Q2 / Q1.50 / 25 = Q2 / 100 ⇒ Q2 = 200 μC. Verification / Alternative check: Linear proportionality is a core assumption in ballistic mode for small angles; experimental plots confirm near-proportional behavior around this range. Why Other Options Are Wrong: 400 μC would quadruple the swing; 50 μC or 25 μC would reduce it; 100 μC would keep it at 25°. Common Pitfalls: Confusing steady-state galvanometers (deflection ∝ current) with ballistic operation (deflection ∝ charge). Final Answer: 200 μC

Question 9

In a strain-gauge–based strain measuring device, what is the practical output quantity of the measurement chain?

Accepted Answer

Introduction / Context: Electrical resistance strain gauges convert mechanical strain into a change in electrical resistance. In practical instruments, this resistance change is most often measured via a Wheatstone bridge, producing a voltage output proportional to strain. Understanding both the transducer variable and the instrumented output clarifies how sensors interface with data-acquisition systems. Given Data / Assumptions: The strain gauge element itself changes resistance ΔR/R ≈ kε, where ε is strain and k is gauge factor. Instrumentation frequently uses a bridge excited by a stable voltage, yielding a small differential voltage proportional to ΔR. Some simple setups may read resistance directly with ohmmeters for static tests. Concept / Approach: The primary transducer output is a resistance change. However, the practical system output (what the user reads) is typically a voltage after the bridge and amplifier. Thus, depending on the readout configuration, one may report either resistance (raw sensor) or voltage (conditioned signal). Step-by-Step Solution: Identify transduction: mechanical strain → ΔR (resistance change).Identify instrumentation: bridge + amplifier → voltage proportional to ΔR.Therefore, the ”output quantity” can be resistance (sensor) or voltage (system). Verification / Alternative check: Commercial strain indicators always specify bridge output in volts or mV/V sensitivity; raw gauge specs give resistance and gauge factor. Why Other Options Are Wrong: ”Impedance” is not the typical descriptor for DC foil gauges; capacitance is unrelated here. Common Pitfalls: Assuming only voltage is correct; overlooking that the fundamental transducer variable is resistance. Final Answer: Either voltage or resistance (depending on readout)

Question 10

What are the fundamental dimensions of magnetic flux density B (Tesla) expressed in M, L, T, and electric current I?

Accepted Answer

Introduction / Context: Dimensional analysis checks the physical consistency of equations and units. Magnetic flux density B is measured in Tesla (T), and relating it to base dimensions helps in deriving or verifying electromagnetic formulas in SI units. Given Data / Assumptions: 1 Tesla = 1 Weber per square metre (Wb/m^2) = 1 Newton per (Ampere·metre) (N/(A·m)). Newton N has dimensions M L T^-2. We examine B in terms of M, L, T, and I. Concept / Approach: Starting from B = N/(A·m), insert dimensions for N and simplify. No length L remains in the numerator after cancellation; the current appears in the denominator as I^1. This produces the standard result used in electromagnetic derivations, e.g., Lorentz force F = q v × B and Ampere's law in SI. Step-by-Step Solution: B = N / (A·m).[N] = M L T^-2; divide by A (current I) and by m (length L).Thus [B] = (M L T^-2) / (I L) = M I^-1 T^-2. Verification / Alternative check: Using B = Wb/m^2 and Wb = V·s = (kg·m^2·s^-3·A^-1)·s gives the same dimensional result after simplification. Why Other Options Are Wrong: Options with L terms or different powers of I or T do not match the base definition N/(A·m). Common Pitfalls: Forgetting that N includes L in the numerator and that an extra L in the denominator comes from the ”per metre”. Final Answer: M I^-1 T^-2

Question 11

Dynamometer wattmeter in an AC circuit: identify what quantity it indicates when connected correctly under sinusoidal steady state.

Accepted Answer

Introduction / Context: Dynamometer wattmeters are widely used for measuring power in alternating-current (AC) circuits. They utilize two coils (current coil and pressure/voltage coil) whose interaction produces torque proportional to the average value of the instantaneous power over a cycle. This question checks your understanding of what an electrodynamometer actually indicates. Given Data / Assumptions: Proper connection of current coil in series and pressure coil across the load. Sinusoidal steady state; instrument constants are idealized. Scale is calibrated in watts. Concept / Approach: The instantaneous torque in a dynamometer wattmeter is proportional to v(t) * i(t). The pointer comes to rest when the average torque over a cycle is balanced by the control spring—hence the deflection is directly proportional to the average value of v(t) * i(t), which is real (true) power P = Vrms * Irms * cosφ. Step-by-Step Solution: Instantaneous power: p(t) = v(t) * i(t).Average over one period: P = (1/T) * ∫ p(t) dt.For sinusoidal steady state, P = V_rms * I_rms * cosφ.Dynamometer deflection ∝ average torque ∝ average power = real power. Verification / Alternative check: If cosφ = 0 (purely reactive), average power is zero and the wattmeter shows nearly zero—matching real power behavior, not apparent or peak power. Why Other Options Are Wrong: rms power / peak power / instantaneous power: not meaningful outputs for wattmeters; the instrument averages over a cycle. apparent power (VA): needs power factor; dynamometer alone does not indicate it. Common Pitfalls: Confusing real power with apparent power. Assuming the pointer shows a snapshot (instantaneous) value; it does not. Final Answer: average power (real power)

Question 12

Voltmeter conversion design: A 100 Ω, 1 mA full-scale movement must be converted to a 0–5 V DC voltmeter. Determine the value of the series multiplier resistor to be added.

Accepted Answer

Introduction / Context: Analog voltmeters are created by adding a series multiplier to a sensitive moving-coil (PMMC) movement. The series resistor limits current so that full-scale deflection occurs at the desired terminal voltage. This problem practices the direct sizing of that multiplier. Given Data / Assumptions: Meter internal resistance Rm = 100 Ω. Full-scale meter current Im = 1 mA = 0.001 A. Desired range Vfs = 5 V. Concept / Approach: At full scale, terminal voltage equals voltage drop across the series resistor plus the internal drop across the movement. Use Ohm’s law to calculate the required series resistor so that total drop equals the target range. Step-by-Step Solution: Total series resistance needed: R_total = Vfs / Im = 5 / 0.001 = 5000 Ω.Multiplier value: Rs = R_total − Rm = 5000 − 100 = 4900 Ω. Verification / Alternative check: Check: At 5 V the current is 5 / (4900 + 100) = 5 / 5000 = 1 mA → full-scale; at lower voltages the deflection is proportional, as expected for a PMMC voltmeter in DC. Why Other Options Are Wrong: 490 Ω / 5100 Ω / 4500 Ω: do not yield 1 mA at 5 V. 5000 Ω: ignores the movement’s internal 100 Ω. Common Pitfalls: Forgetting to subtract the meter resistance from the total resistance required. Confusing mA with A when computing R_total. Final Answer: 4900 Ω

Question 13

Reading of a dynamometer wattmeter connected in an AC circuit: determine what the instrument indicates under normal operation.

Accepted Answer

Introduction / Context: An electrodynamometer wattmeter has a current coil in series with the load and a pressure coil across it. The interaction torque is proportional to the product of instantaneous voltage and current averaged over a cycle. The question asks which power quantity the pointer shows in AC. Given Data / Assumptions: AC steady state; frequency is constant. Proper connections and instrument calibration. Concept / Approach: Average (real) power in an AC circuit is P = V_rms * I_rms * cosφ. The dynamometer’s average torque is proportional to this P, so its steady reading corresponds to true power. Apparent power S = V_rms * I_rms differs by the power factor and cannot be read directly from a single wattmeter. Step-by-Step Solution: Instantaneous torque ∝ v(t) * i(t).Average over a cycle → pointer deflection ∝ average of v(t) * i(t).Therefore, reading equals true power in watts. Verification / Alternative check: For a pure inductor (cosφ ≈ 0), the wattmeter reads nearly zero, confirming it measures real—not apparent—power. Why Other Options Are Wrong: Apparent/peak/instantaneous/rms power are different quantities; the instrument is not designed to indicate these directly. Common Pitfalls: Equating wattmeter reading to VA without accounting for power factor. Final Answer: average power (true power)

Question 14

In figure the bridge is balanced when Z4 is

Accepted Answer

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Question 15

Choosing an appropriate voltmeter: which instrument specification minimizes loading when measuring the voltage across a 20 kΩ resistor?

Accepted Answer

Introduction / Context: When measuring voltage across a component, the voltmeter should draw negligible current so that the circuit under test is not disturbed. Sensitivity in kΩ/V (for analog meters) indicates the input resistance per volt of range; higher sensitivity means higher input resistance and less loading. Given Data / Assumptions: Measured element: 20 kΩ resistor. Analog voltmeters characterized by sensitivity (kΩ/V). We seek the highest practical input resistance compared with 20 kΩ. Concept / Approach: Loading error is minimized when R_meter ≫ R_load. For a sensitivity S (kΩ/V) on a V-range, R_meter = S * V (in kΩ). A 10 kΩ/V meter on, say, a 10 V range has 100 kΩ input—five times the 20 kΩ load—resulting in reasonable accuracy compared to a 1 kΩ/V meter (only 10 kΩ on 10 V range) or a fixed 5 kΩ instrument. Step-by-Step Solution: Assume a 10 V range example: R_meter(10 kΩ/V) = 10 * 10 kΩ = 100 kΩ.Parallel of 20 kΩ with 100 kΩ ≈ 16.7 kΩ → only ~16% reduction, acceptable for many purposes.For 1 kΩ/V on 10 V, R_meter = 10 kΩ → heavy loading (effective ≈ 6.7 kΩ).5 kΩ fixed is worse; equal to 20 kΩ is still not “≫”. Verification / Alternative check: Digital voltmeters typically have 10 MΩ input, giving negligible loading; among the given analog choices, 10 kΩ/V is the best to reduce error. Why Other Options Are Wrong: 5 kΩ and 1 kΩ/V lead to substantial current draw and large measurement error. Equal to 20 kΩ still causes 50% voltage division error. “None” is incorrect because a suitable option exists. Common Pitfalls: Ignoring how sensitivity and selected range determine input resistance. Final Answer: Voltmeter with sensitivity of 10 kΩ/V

Question 16

Why the DC potentiometer method is more accurate than a direct voltmeter reading: identify the primary reason related to circuit loading.

Accepted Answer

Introduction / Context: DC potentiometers determine an unknown electromotive force (EMF) by balancing it against a known, adjustable reference drop along a calibrated resistor. At balance (null), no current is drawn from the unknown source, which eliminates loading error that occurs with finite-impedance voltmeters. Given Data / Assumptions: Null-balance condition is achieved (galvanometer shows zero deflection). Reference supply and wire are properly standardized with a known cell. Concept / Approach: With no current drawn from the unknown EMF at balance, the measured value equals its open-circuit value. A voltmeter, even a high-impedance one, draws some current and thus can slightly reduce the measured voltage of a high-source-resistance circuit. Therefore, potentiometers provide superior accuracy for small or delicate sources. Step-by-Step Solution: Connect unknown source to the potentiometer via a galvanometer.Adjust the sliding contact until galvanometer indicates zero (null current).Read EMF using the calibrated length × current (or directly the scale).Since i_unknown = 0 at null, loading error = 0. Verification / Alternative check: Comparisons with high-quality digital voltmeters show agreement; deviations arise only from calibration errors, not loading, validating the principle. Why Other Options Are Wrong: Options (a) and (b) contradict the null method. (d) Centre-zero galvanometer is an indicator, not the reason for accuracy. (e) Potentiometers do not integrate to average noise. Common Pitfalls: Assuming “infinite” DVM input means identical accuracy—source loading can still matter for very high source resistance or microvolt-level sources. Final Answer: it does not load the circuit at all (null-balance measurement)

Question 17

Thermocouple measurement practice: which instrument is preferred to read the small output EMF produced by a thermocouple temperature sensor?

Accepted Answer

Introduction / Context: Thermocouples generate small direct-current voltages (often a few millivolts) proportional to temperature difference at the junction. Accurately measuring these tiny EMFs requires an instrument with both high sensitivity (millivolt range) and high input resistance to avoid loading the sensor. Given Data / Assumptions: Thermocouple EMF magnitude: typically 1–50 mV depending on type and temperature. Source resistance can be several ohms to tens of ohms. Desired instrument should not load the thermocouple and must resolve millivolts. Concept / Approach: Choose an instrument whose input resistance is large compared with the source resistance and whose range matches millivolt levels. A high-resistance milli-voltmeter provides both: millivolt scaling and minimal loading, yielding accurate readings or conditioning for further processing. Step-by-Step Solution: Recognize signal level: EMF ≈ mV → need mV range.Avoid loading: choose instrument with high input resistance (≫ sensor resistance).Therefore: select a high-resistance milli-voltmeter. Verification / Alternative check: Modern practice often uses instrumentation amplifiers with mega-ohm inputs feeding ADCs; functionally this emulates a high-resistance millivoltmeter, confirming the choice. Why Other Options Are Wrong: High-resistance ammeter measures current, not suitable for mV EMFs. High-resistance voltmeter (on higher ranges) may lack millivolt sensitivity. Moving-iron AC voltmeters are for AC and are insensitive at millivolt DC levels. Common Pitfalls: Using general-purpose voltmeter with insufficient resolution, leading to large quantization or scale errors. Final Answer: high resistance milli-voltmeter

Question 18

Turning a digital frequency counter into a digital voltmeter (DVM): which additional block enables voltage measurement?

Accepted Answer

Introduction / Context: A digital frequency counter inherently counts pulses in a given gate time to report frequency. If the input voltage can be converted into a proportional frequency, the same counting mechanism becomes a digital voltmeter. This is the principle behind voltage-to-frequency (V-F) conversion DVMs. Given Data / Assumptions: We have a standard frequency counter with gating and counting circuitry. We need a block that converts an analog voltage into a frequency. Concept / Approach: A voltage-controlled oscillator (VCO) produces an output frequency proportional to an input control voltage. By scaling and linearizing the VCO, the counter’s reading (counts within the gate time) becomes directly proportional to the input voltage. Average-value noise rejection is also improved due to time averaging in counting. Step-by-Step Solution: Insert VCO → f_out = k * V_in.Feed f_out to the frequency counter.Counter displays counts per gate → proportional to V_in → acts as DVM. Verification / Alternative check: Commercial V-F converter ICs (or VCOs inside PLLs) are commonly used to implement integrating DVMs and telemetry systems—confirming the approach. Why Other Options Are Wrong: D/A converter and power amplifier do not perform voltage-to-frequency conversion. Operational amplifier alone cannot convert voltage to frequency without additional timing components. PLL without a VCO cannot generate frequency proportional to input voltage. Common Pitfalls: Confusing V-F conversion with A-D conversion using successive approximation or dual-slope methods (different architectures). Final Answer: voltage controlled oscillator

Question 19

Assertion–Reason (connection choice for wattmeter on low-impedance loads): Decide the truth of the following statements. Assertion (A): For low-impedance loads, the wattmeter pressure (voltage) coil is connected directly across the load. Reason (R):…

Accepted Answer

Introduction / Context: There are two practical connection schemes for a dynamometer wattmeter—voltage coil on the load side or on the supply side of the current coil. The choice is made to minimize measurement error for particular load conditions. Given Data / Assumptions: Low-impedance load implies high current and relatively low voltage drop across the load. The current coil has a small but non-negligible resistance causing a voltage drop. We seek to minimize errors due to including the current-coil drop in the measured voltage. Concept / Approach: For low-impedance (high-current) loads, connecting the pressure coil across the load avoids adding the current-coil voltage drop to the measured voltage. This reduces error. Separately, a wattmeter measures true power, not apparent power; its indication is P = V_rms * I_rms * cosφ, not V_rms * I_rms. Step-by-Step Solution: Assess Assertion: Correct—pressure coil across the load minimizes error from current-coil drop.Assess Reason: Incorrect—a wattmeter measures average (real) power, not apparent power.Therefore: A is true and R is false. Verification / Alternative check: Textbook connection rules: for low-impedance loads use “load-side” connection; for high-impedance/low-current loads the supply-side connection can be preferable to reduce current drawn by the pressure coil through the current coil branch. Why Other Options Are Wrong: Any option implying R is true misstates the wattmeter function. Options making A false contradict standard practical guidance. Common Pitfalls: Confusing real and apparent power; the wattmeter does not show V*A. Assuming one connection suits all loads; connection choice depends on load impedance. Final Answer: A is true R is false

Question 20

Identify the transformer type: which transformer normally operates with its secondary nearly short-circuited under standard conditions?

Accepted Answer

Introduction / Context: Instrument transformers scale primary quantities to safe measurable levels. Current transformers (CTs) provide a secondary current proportional to primary current and are designed to work with very low secondary burden (nearly short circuit). Recognizing this operating requirement is vital for safety and accuracy. Given Data / Assumptions: Normal operation of a CT: secondary connected to an ammeter or burden rated in VA, with very low impedance. Open-circuiting a CT secondary is dangerous due to high induced voltage. Concept / Approach: A CT behaves like a current source; to maintain magnetizing current small, its secondary must be close to short circuit so that the exciting voltage is low. In contrast, potential transformers and power/distribution transformers are voltage sources intended to feed specified loads at rated voltage, not a short circuit. Step-by-Step Solution: Identify which transformer expects near-zero secondary impedance → CT.Others (PT, distribution, power, isolation) are not operated with the secondary shorted. Verification / Alternative check: Practical rule: never open-circuit a CT secondary; keeping it shorted (or on rated burden) is mandatory for safety and accuracy—corroborating the selection. Why Other Options Are Wrong: PT and power/distribution transformers must not be short-circuited in service; that would cause large fault currents. Isolation transformer behaves like a standard power transformer; not short-circuited. Common Pitfalls: Confusing CTs with PTs; remember CT ≈ current source, PT ≈ voltage source. Final Answer: Current transformer (CT)

Measurements and Instrumentation Questions