Question 1

In pulse and digital electronics, which type of circuit is specifically designed to produce very short-duration spikes (narrow pulse triggers) from an input signal or event?

Accepted Answer

Introduction: Short-duration spikes, often called trigger pulses or narrow pulses, are essential in timing, synchronization, counting, and digital control. This question checks recognition of the circuit class whose primary function is to create sharp, brief pulses on demand, rather than to average, integrate, or otherwise reshape signals into long-duty cycles. Given Data / Assumptions: The target pulse must be narrow (short time width) with a quick rise and fall. Applications include clocking flip-flops, triggering monostables, or providing synchronization edges. We are selecting among distinct functional blocks used in basic electronics. Concept / Approach: A trigger pulse generator is explicitly built to deliver narrow pulses. Implementations range from differentiator-based edge generators with diode shaping, to Schmitt-trigger RC networks, to monostable multivibrators (one-shots) set for small time constants. By contrast, integrators emphasize area/averaging, and DC converters emphasize producing a steady level rather than a spike. Step-by-Step Solution: 1) Identify the required output: a narrow pulse (spike) suitable for triggering.2) Map candidate circuits to function: integrators average, converters rectify/average, timing blocks may produce long intervals.3) Choose the class designed for short pulses: the trigger pulse generator.4) Conclude that the correct answer is the purpose-designed generator of narrow pulses. Verification / Alternative check: Consider a monostable multivibrator configured with a small RC constant; it outputs a short pulse when triggered. This is a canonical trigger pulse generator use-case and matches the requirement. Why Other Options Are Wrong: RL integrator: shapes/averages signals rather than producing sharp, adjustable trigger spikes. Timing circuit: generic term; often used for long intervals rather than intentionally minimal widths. Pulse waveform-to-dc converter: averages or rectifies a pulse train into a DC level, not spikes. Monolithic voltage regulator: provides regulated DC voltage, not pulses. Common Pitfalls: Equating any RC network with a pulse generator. Differentiators can produce edges, but a dedicated trigger pulse generator includes amplitude control, shaping, and consistent pulse width across conditions. Final Answer: A trigger pulse generator

Question 2

Which statements about an ideal capacitor's behavior are correct in circuit theory (choose the best overall statement)?

Accepted Answer

Introduction: Capacitors are energy-storage elements whose current-voltage relationship is i = C * dv/dt. This relationship yields several widely used rules of thumb about transient and steady-state behavior. The question asks you to identify the consolidated truth among the listed statements. Given Data / Assumptions: Ideal capacitor with capacitance C (no leakage, ESR, or ESL). Standard circuit-theory interpretations of "instantaneous" and "dc steady state". Small-signal, linear operating region. Concept / Approach: Because i = C * dv/dt, an instantaneous voltage step (large dv/dt) implies a very large current impulse; conversely, changing the capacitor's voltage requires time (non-instantaneous) unless infinite current is available. In dc steady state (dv/dt = 0), the current is zero, so the ideal capacitor behaves as an open circuit. Step-by-Step Solution: 1) Voltage cannot jump instantly: that would require infinite current since dv/dt would be infinite.2) For fast transients, the capacitor presents very low impedance, effectively shunting rapid changes and acting "like a short" for the highest-frequency components.3) At dc steady state, dv/dt = 0, so i = 0 and the capacitor behaves as an open circuit.4) Therefore, each individual statement is correct; the combined best choice is "All of the above". Verification / Alternative check: Frequency-domain view: Xc = 1 / (2 * pi * f * C). As f → ∞, Xc → 0 (short-like). As f → 0 (dc), Xc → ∞ (open-like). This confirms the time-domain reasoning. Why Other Options Are Wrong: Any single statement alone (a, b, or c) is incomplete; the question asks for the best comprehensive truth. None of the above: contradicts standard capacitor behavior taught in basic circuit theory. Common Pitfalls: Confusing "short to instantaneous changes" with "short to all AC". Real capacitors have finite impedance and parasitics; only very high-frequency components see near-short behavior. Final Answer: All of the above

Question 3

In a simple RC integrator, if the capacitor accidentally becomes shorted (zero impedance), what happens to the output measured across the capacitor node?

Accepted Answer

Introduction: An RC integrator typically consists of a series resistor feeding a capacitor to ground, with the output taken across the capacitor. This question explores the failure mode when the capacitor is shorted, a common troubleshooting scenario that produces a distinctive symptom at the output node. Given Data / Assumptions: Passive RC integrator: input → series R → node → capacitor to ground, output at the node. Steady operation with a bounded input signal. "Shorted capacitor" means the capacitor's impedance has collapsed to ~0 Ω. Concept / Approach: If the shunt element (capacitor) is a short, the output node is directly clamped to ground potential. Regardless of the input waveform, the node voltage cannot rise above approximately 0 V because any attempted change is immediately diverted to ground through the short. Step-by-Step Solution: 1) In a healthy RC integrator, the capacitor charges/discharges, creating an output proportional to the time-integral of the input.2) With a shorted capacitor, the output node is effectively a direct connection to ground.3) Therefore, the measured output voltage is ≈ 0 V for all practical purposes.4) The circuit no longer integrates; the input sees a series resistor into a ground short, which may stress the source. Verification / Alternative check: Measure with a multimeter or oscilloscope: the node reads near 0 V despite input changes. Upstream, current is limited only by the series resistor, confirming the fault signature. Why Other Options Are Wrong: Same as input: impossible; the node is clamped to ground. None of the above: incorrect because 0 V is the expected reading. Is at ground vs would measure zero volts: both descriptions point to 0 V, but the most precise measurement-oriented choice is "would measure zero volts". Common Pitfalls: Assuming the integrator will simply "stop integrating" but still pass some signal. A hard short forces the output to 0 V; any remaining signal appears only as current through the series resistor. Final Answer: would measure zero volts

Question 4

For an RC differentiating circuit driven by a periodic pulse waveform, which statement correctly captures the two possible regimes relating the pulse width (tw) to the circuit time constant (tau)?

Accepted Answer

Introduction: In RC differentiators, performance depends on comparing the input pulse width tw to the circuit time constant tau = R * C. Designers commonly distinguish between "long" pulses (tw much greater than tau) and "short" pulses (tw much less than tau) to anticipate output spike shapes and amplitudes. Given Data / Assumptions: First-order RC differentiator with time constant tau. Periodic pulse input with width tw and period Tperiod (not used directly here). Rule-of-thumb boundary at ~5 * tau separates long and short regimes. Concept / Approach: When tw ≥ 5 * tau, the capacitor has time to charge and discharge substantially within each pulse edge, yielding narrow, well-defined spikes primarily at transitions. When tw < 5 * tau, the circuit operates in a strongly differentiating regime where the output resembles brief spikes with limited decay during the pulse, emphasizing edges over the flat top. Step-by-Step Reasoning: 1) Define tau = R * C as the characteristic time scale.2) For tw ≥ 5 * tau, treat the pulse as "long"; the capacitor's exponential response largely settles between edges.3) For tw < 5 * tau, treat the pulse as "short"; output is dominated by edge spikes, with minimal settling between edges.4) Hence the two practical conditions are tw ≥ 5 * tau or tw < 5 * tau. Verification / Alternative check: Simulate with typical values (e.g., R = 1 kΩ, C = 1 nF → tau = 1 µs). Compare outputs for tw = 10 µs (≥ 5 * tau) versus tw = 0.2 µs (< 5 * tau). The first shows distinct charge/discharge, the second shows sharp, narrow spikes. Why Other Options Are Wrong: Options a and b omit the complementary short-pulse regime or duplicate the same inequality; option c covers only short cases; option e is a single value and not a regime. Common Pitfalls: Treating 5 * tau as an exact boundary; it is a heuristic. Real component tolerances and loading shift the practical split, but the two regimes remain conceptually valid. Final Answer: tw ≥ 5Τ or tw < 5Τ

Question 5

Filter behavior mapping: An RL integrator behaves as which kind of first-order filter, and an RC differentiator behaves as which kind, respectively?

Accepted Answer

Introduction: First-order RL and RC networks can be arranged to integrate or differentiate signals. Each arrangement corresponds to a classic filter response, useful for quick intuition about frequency-domain behavior and for selecting components in signal conditioning. Given Data / Assumptions: RL integrator topology: output taken so that low-frequency components are passed and fast changes are attenuated. RC differentiator topology: output taken so that high-frequency transitions are emphasized. Linear, time-invariant approximation with ideal components. Concept / Approach: Integrators pass low-frequency components (they "accumulate" slowly varying signals) and attenuate high-frequency content, which is the hallmark of a low-pass filter. Differentiators emphasize rapid changes—high-frequency components—while attenuating slow variations, the hallmark of a high-pass filter. Step-by-Step Solution: 1) RL integrator: with appropriate node selection, the inductor resists rapid current changes; the output follows the averaged (integrated) behavior, passing lows → low-pass.2) RC differentiator: the capacitor's impedance decreases with frequency, creating spikes at edges and passing highs → high-pass.3) Therefore, the correct mapping is low-pass for the RL integrator and high-pass for the RC differentiator.4) This mapping aligns directly with Bode magnitude slopes: ±20 dB/dec around the cutoff. Verification / Alternative check: Frequency-domain impedances: Xl = 2 * pi * f * L increases with f (blocking highs in the integrator path); Xc = 1 / (2 * pi * f * C) decreases with f (passing highs in the differentiator path). The resulting transfer functions match low-pass and high-pass behaviors, respectively. Why Other Options Are Wrong: Low-pass, low-pass / high-pass, high-pass: both entries cannot simultaneously describe integrator and differentiator behavior. High-pass, low-pass: reverses the correct mapping. Band-pass, band-stop: require at least second-order behavior or combined networks, not simple first-order integrator/differentiator forms. Common Pitfalls: Confusing where the output is taken in the network; swapping nodes can convert an apparent integrator into a different response. Always confirm topology and node definitions. Final Answer: low-pass, high-pass

Question 6

The output voltage of an RC integrator will eventually equal the voltage of a single input pulse if the input pulse width is less than 5 time constants.

Accepted Answer

False

Question 7

A differentiator circuit can be used to convert a pulse input to a nearly constant dc output.

Accepted Answer

False

Question 8

During the steady-state condition of a differentiator, the average output voltage is zero volts.

Accepted Answer

True

Question 9

The voltage across a capacitor in an RC integrator circuit cannot change exponentially; it can change only instantaneously.

Accepted Answer

False

Question 10

The output voltage of a differentiator goes negative on the falling edge of the input pulse.

Accepted Answer

True

Question 11

The output of a differentiator could be considered a spike when the input pulse width is much longer than 5 time constants.

Accepted Answer

True

Question 12

The steady-state condition of an integrator is reached after 5 time constants regardless of the number of input pulses that occur in that amount of time.

Accepted Answer

True

Question 13

The output of an RC differentiator is taken from across the capacitor.

Accepted Answer

False

Question 14

If the output of an RC integrator is zero volts, the capacitor might be open.

Accepted Answer

False

Question 15

A repetitive pulse with a 50% duty cycle is being applied to the input of an RC integrator. If one time constant is less than one-fifth the pulse width, the capacitor will be able to fully charge and discharge.

Accepted Answer

True

Question 16

The output of an RL differentiator is taken from across the inductor.

Accepted Answer

True

Question 17

If a repetitive-pulse waveform is applied to an RC integrator, the output waveshape depends on the relationship of the circuit time constant and the duty cycle of the input pulses.

Accepted Answer

False

Question 18

For a capacitor to completely charge in an RC integrator, the pulse width must be _____ 5 time constants.

Accepted Answer

greater than or equal to

Question 19

If the pulse width were cut in half in the given circuit, the voltage across the resistor would be ______ at the end of the pulse.

Accepted Answer

0.46 V

Question 20

If the pulse source has an internal resistance of 80 Ω in the given circuit, it will take ______ for the output voltage to decrease to zero.

Accepted Answer

1.1 ms

Time Response of Reactive Circuits Questions