ECE 201 Foundations of Electric Circuits I - Final Exam Review (Qns & Ans) - DU 2025, Exams of Electronic Circuits Design

Download ECE 201 Foundations of Electric Circuits I - Final Exam Review (Qns & Ans) - DU 2025 and more Exams Electronic Circuits Design in PDF only on Docsity!

ECE 201

Foundations of Electric Circuits I

Final Exam Review

(Questions & Solutions)

Section I – Multiple Choice (Questions 1–8) Question 1: Which law states that the algebraic sum of voltages around any closed loop in a circuit is zero? A. Ohm’s Law B. Kirchhoff’s Voltage Law (KVL) C. Kirchhoff’s Current Law (KCL) D. Thevenin’s Theorem ANS : B Rationale: Kirchhoff’s Voltage Law (KVL) asserts that the sum of the electrical potential differences (voltages) around any closed loop in a circuit equals zero, ensuring energy conservation in electrical circuits.

---

Question 2: The process of converting an entire circuit into an equivalent voltage source with a series resistance is known as: A. Norton's Theorem B. Superposition C. Thevenin’s Theorem D. Millman’s Theorem ANS : C Rationale: Thevenin’s Theorem allows any linear circuit to be reduced to a single voltage source in series with a resistance, greatly simplifying circuit analysis.

---

Question 3:

C. R/C

D. 1/(R · C)

ANS : B

Rationale: The time constant τ in a resistor–capacitor (RC) circuit is computed as the product of resistance (R) and capacitance (C). It characterizes the rate at which the capacitor charges or discharges.

---

Question 6: In sinusoidal steady‑state analysis, the phasor impedance of an inductor is represented by: A. ωL B. −jωL C. jωL D. 1/(jωL) ANS : C Rationale: In the phasor domain, the impedance of an inductor is expressed as ( Z_L = jωL ), where ( ω ) is the angular frequency and ( L ) is the inductance.

---

Question 7: When converting a time‑domain circuit to the s‑domain for analysis, which mathematical transform is applied? A. Fourier Transform B. Z‑Transform C. Laplace Transform D. Hilbert Transform ANS : C Rationale: The Laplace Transform is used to convert time‑domain

circuit equations into the s‑domain, simplifying the analysis of circuits with transient behavior by representing differential equations as algebraic equations.

---

Question 8: Which of the following is an advantage of using the node-voltage method in circuit analysis? A. It is always the simplest method for any circuit. B. It directly applies Kirchhoff’s Voltage Law to loops. C. It reduces the number of equations for circuits with many nodes relative to meshes. D. It does not require the knowledge of resistor values. ANS : C Rationale: The node-voltage method uses Kirchhoff’s Current Law (KCL) to set up equations at the nodes and is particularly advantageous in circuits with many nodes that result in fewer simultaneous equations compared to mesh analysis.

---

Section II – Fill-in-the-Blank (Questions 9–14) Question 9: In circuit analysis, the law stating that the sum of currents entering a node equals the sum of currents leaving that node is known as _______ Law. ANS : Kirchhoff’s Current Rationale: Known as Kirchhoff’s Current Law (KCL), this principle ensures conservation of charge at a circuit node.

---

Rationale: KVL is based on the principle of energy conservation, requiring that the algebraic sum of all voltage drops around a closed loop is zero.

---

Question 14: When using Thevenin’s theorem, the circuit is reduced to a single voltage source in series with an equivalent _______ seen from the load terminals. ANS : resistance Rationale: Thevenin’s theorem replaces a complex network by a single voltage source (V_TH) and a series resistance (R_TH), simplifying analysis at the load.

---

Section III – True/False (Questions 15–18) Question 15: True or False: In a DC circuit, the open-circuit voltage across two points is always equal to the Thevenin equivalent voltage seen from those points. ANS : True Rationale: By definition, the Thevenin voltage is the open-circuit voltage at the load terminals, making the statement true.

---

Question 16: True or False: The Norton equivalent circuit is the dual of the Thevenin equivalent circuit. ANS : True Rationale: Norton's theorem states that any linear electrical network with voltage and current sources can be replaced by an equivalent current source in parallel with a resistor, which is mathematically dual to

Thevenin’s equivalent circuit.

Question 17: True or False: In an RC circuit, the capacitor voltage cannot change instantaneously at the moment of a switching event. ANS : True Rationale: Due to the inherent energy storage properties of a capacitor and its inability to change voltage instantaneously, the capacitor voltage remains continuous at the switching instant.

---

Question 18: True or False: Mesh analysis typically requires fewer equations than node-voltage analysis in circuits with many current sources. ANS : False Rationale: Mesh analysis generally works best for circuits with many voltage sources, whereas node-voltage analysis is often more efficient in circuits with numerous current sources. Therefore, the statement is false.

---

Section IV – Multiple Response (Questions 19–30) Question 19: Which of the following are recognized as fundamental circuit theorems? (Select all that apply.) A. Thevenin’s Theorem B. Norton’s Theorem C. Superposition Theorem D. Millman’s Theorem E. Euler’s Theorem

ANS : A, B, C

Rationale: In the Laplace domain, ( s = \sigma + j\omega ) where ( \sigma ) represents damping and ( j\omega ) represents the oscillatory part. It is used for transforming time-domain circuit equations into algebraic equations; it is not strictly ( j\omega ) except under sinusoidal steady state.

---

Question 22: Consider a series RC circuit (“first-order circuit”). Which statements about its transient response are true? (Select all that apply.) A. The time constant is given by ( \tau = R \times C ). B. The capacitor voltage is zero at ( t = 0 ) if the capacitor is initially discharged. C. The current decays exponentially with time. D. The capacitor eventually charges to the source voltage in a DC circuit. E. Transient response is independent of the resistor value. ANS : A, B, C, D Rationale: For a series RC circuit, ( \tau = R \times C ), an initially uncharged capacitor will have zero voltage at ( t = 0 ), and the current decays exponentially as the capacitor charges to the source voltage. The resistor value directly affects the time constant, making statement E false.

---

Question 23: In sinusoidal steady‑state analysis using phasors, which statements are correct? (Select all that apply.) A. Differential equations are transformed into algebraic equations. B. Every sinusoidal signal is represented by a magnitude and phase angle.

C. All sinusoids must have the same angular frequency for phasor analysis to be valid. D. Phasor analysis eliminates explicit time dependence in the analysis. E. It is applicable only to linear circuits. ANS : A, B, C, D, E Rationale: Phasor analysis converts differential equations to algebraic ones by representing sinusoids (with identical frequencies) by magnitude and phase, thereby eliminating time as an explicit variable, and is applicable only to linear circuits.

---

Question 24: Which assumptions are made when applying Kirchhoff’s Current Law (KCL) in circuit analysis? (Select all that apply.) A. Charge conservation B. The node is treated as having negligible physical size C. The circuit is lumped (wires are ideal) D. All currents entering and leaving are instantaneous E. Voltage sources always have zero internal resistance ANS : A, B, C Rationale: KCL is based on the conservation of charge, assumes that the node has negligible size (lumped circuit assumption), and that currents can be summed instantaneously. Option D is a simplification error, and E is irrelevant to KCL applicability.

---

Question 25: For transient analysis in an RC circuit, which of the following techniques can be applied? (Select all that apply.) A. Formulating and solving differential equations B. Using the Laplace Transform

A. Remove the load resistor at the point of interest. B. Determine the open-circuit voltage across the load terminals. C. Calculate the equivalent resistance seen from the load terminals, deactivating all independent sources. D. Use the Norton equivalent in all cases instead. E. Replace independent sources with their internal resistances (voltage sources shorted, current sources opened). ANS : A, B, C, E Rationale: Thevenin’s theorem requires removing the load, finding the open-circuit voltage, and calculating the equivalent resistance by deactivating independent sources (voltage - > short, current - > open). Option D is incorrect because Norton’s theorem is an alternative form.

---

Question 28: Mesh analysis is most effective when applied to circuits with which characteristics? (Select all that apply.) A. The circuit is planar B. There are few meshes relative to the number of nodes C. The circuit contains many current sources in parallel D. Loop currents can be easily defined and calculated E. The circuit has multiple voltage sources that simplify mesh equations ANS : A, B, D, E Rationale: Mesh analysis is best applied to planar circuits with fewer independent loops, where loop currents are clearly defined and the presence of voltage sources simplifies KVL equations. Parallel current sources are better analyzed using the node-voltage method.

---

Question 29: Which of the following elements are considered energy storage

components in electric circuits? (Select all that apply.) A. Capacitors B. Inductors C. Resistors D. Batteries E. Transformers ANS : A, B, D Rationale: Capacitors, inductors, and batteries store energy (in electric, magnetic, and chemical forms, respectively). Resistors dissipate energy, and while transformers store magnetic energy transiently, they are primarily energy transfer devices.

---

Question 30: Which factors directly affect the time constant in a first‑order circuit? (Select all that apply.) A. The resistance value B. The capacitance (or inductance) value C. The initial conditions of the circuit D. Temperature if it alters component values E. The frequency of the applied input signal ANS : A, B, D Rationale: The time constant in an RC circuit is ( \tau = R \times C ) (and for an RL circuit, ( \tau = \frac{L}{R} )), so it depends on resistance and the capacitance/inductance. Temperature can affect component parameters, thus indirectly affecting the time constant. The initial conditions and applied frequency do not alter the time constant itself.

dependent sources do not violate linearity. Multiple Response: Which of the following are valid methods for analyzing a circuit? (Select all that apply) a) Nodal Analysis b) Mesh Analysis c) Source Transformation d) Phasor Analysis Correct ANS : a), b), c), d) Rationale: All listed methods are standard techniques for circuit analysis. Multiple Choice: What is the Thevenin equivalent resistance (( R_{th} )) of a circuit if the open-circuit voltage (( V_{oc} )) is ( 20\ V ) and the short-circuit current (( I_{sc} )) is ( 2\ A )? a) ( 5\ \Omega ) b) ( 10\ \Omega ) c) ( 20\ \Omega ) d) ( 40\ \Omega ) Correct ANS : b) ( 10\ \Omega ) Rationale: ( R_{th} = \frac{V_{oc}}{I_{sc}} ). Fill-in-the-Blank: The Norton equivalent circuit consists of a current source in parallel with a __.

Correct ANS : resistance Rationale: The Norton equivalent replaces the original circuit with a current source and a parallel resistance. True/False: In an ideal inductor, the voltage leads the current by ( 90 ) degrees. Correct ANS : True Rationale: This is a fundamental property of inductors in AC circuits. Multiple Response: Which of the following are characteristics of an ideal operational amplifier (op-amp)? (Select all that apply) a) Infinite input impedance b) Zero output impedance c) Infinite open-loop gain d) Zero input bias current Correct ANS : a), b), c), d) Rationale: These are the defining ideal characteristics of an op-amp. Multiple Choice: What is the equivalent capacitance of two capacitors, ( C_1 = 10\ \mu F ) and ( C_2 = 20\ \mu F ), connected in series? a) ( 5\ \mu F ) b) ( 10\ \mu F ) c) ( 15\ \mu F ) d) ( 30\ \mu F ) Correct ANS : a) ( 6.67\ \mu F )

In a first-order RC circuit, the time constant (( \tau )) is given by: a) ( \tau = RC ) b) ( \tau = \frac{R}{C} ) c) ( \tau = \frac{C}{R} ) d) ( \tau = \frac{1}{RC} ) Correct ANS : a) ( \tau = RC ) Rationale: This is the standard formula for the time constant in an RC circuit. Fill-in-the-Blank: The quality factor (Q) of a series RLC circuit at resonance is a measure of its __. Correct ANS : selectivity Rationale: The Q factor indicates how sharply the circuit resonates at its resonant frequency. True/False: The current through an inductor changes instantaneously. Correct ANS : False Rationale: The current through an inductor cannot change instantaneously due to the inductor's property of opposing changes in current. Multiple Response: Which of the following are benefits of using phasors in circuit analysis? (Select all that apply) a) Simplifies the analysis of AC circuits

b) Converts differential equations into algebraic equations c) Allows for the use of impedance d) Provides a time-domain solution directly Correct ANS : a), b), c) Rationale: Phasors simplify AC analysis by transforming sinusoidal signals into complex numbers, making calculations easier. They do not directly provide time-domain solutions. Multiple Choice: What is the voltage across a ( 5\ \Omega ) resistor if ( 2\ A ) of current flows through it? a) ( 2.5\ V ) b) ( 5\ V ) c) ( 10\ V ) d) ( 15\ V ) Correct ANS : c) ( 10\ V ) Rationale: Using Ohm's Law: ( V = IR ). Fill-in-the-Blank: Kirchhoff's Current Law (KCL) states that the sum of currents entering a node is equal to the sum of currents __ the node. Correct ANS : leaving Rationale: KCL is based on the conservation of charge. True/False: The voltage across a capacitor in a DC circuit is constant after the transient response has settled.