Question 1

Branch current method (circuit analysis): Which pair of laws or theorems is directly applied when solving networks using the branch current method?

Accepted Answer

Introduction / Context: The branch current method is a systematic way to analyze circuits by assuming currents in each branch and writing equations based on conservation and element relationships. It is especially effective in multi-node resistive networks, where direct application of laws reduces the problem to solvable linear equations. Given Data / Assumptions: A general resistive network with identifiable branches and nodes. We wish to determine which fundamental principles underpin the branch current method. Concept / Approach: Two ingredients are used: Kirchhoff's Current Law (KCL), which enforces current conservation at nodes, and Ohm's law, which relates voltage and current for resistive elements. KVL emerges implicitly when KCL and element laws are applied around the network, but the explicit setup centers on KCL at nodes and Ohm's law on branches. Step-by-Step Solution: Assign algebraic directions to branch currents (arbitrary but consistent).Write KCL at independent nodes: sum of currents leaving/entering each node equals zero.Express each branch current using Ohm's law: I = V/R (or V = I * R) with appropriate polarities.Solve the resulting linear system for unknown branch currents. Verification / Alternative check: After solving, check KVL around loops (sum of voltage rises and drops equals zero) as a consistency test. Correct KCL and Ohm's-law modeling will satisfy KVL automatically in linear resistive networks. Why Other Options Are Wrong: Kirchhoff's voltage and current laws: KVL isn't the direct setup tool here; KCL is primary along with Ohm's law. Thevenin's and superposition theorems: Useful alternatives, but not the essence of the branch current method. Common Pitfalls: Mistaking loop-current (mesh) method—which uses KVL—as the branch current method. Final Answer: Kirchhoff's current law and Ohm's law

Question 2

Assigning assumed current directions in analysis: When defining branch current directions before writing equations, which statement is true?

Accepted Answer

Introduction / Context: In nodal or branch-current analysis, we often assume directions for unknown currents to set up equations. Learners sometimes worry about picking the 'right' direction, but the mathematics automatically corrects the sign if the initial assumption is opposite to the actual direction. Given Data / Assumptions: We are assigning directions for unknown branch currents before applying KCL/KVL. Linear, time-invariant resistive network. Concept / Approach: Directions are arbitrary but must be consistent. After setting directions, apply KCL and Ohm's law. If the computed value of a current is negative, it simply means the real current flows opposite to the assumed direction. Therefore, correctness does not depend on the initial arrow choices, only on consistency. Step-by-Step Solution: Choose a direction for each unknown branch current (e.g., left-to-right).Write KCL at nodes using the chosen directions.Solve for branch currents; allow negative results to indicate reversal.Interpret signs after solution to understand actual current directions. Verification / Alternative check: Try flipping one assumed branch direction and re-solve; equation signs change accordingly, but the physical results (magnitudes and true directions) remain consistent, confirming that initial choices are not critical. Why Other Options Are Wrong: 'critical': Suggests only one correct initial choice; not true. 'must point into a node' / 'must point out of a node': Arbitrary constraints; either convention works as long as it is applied consistently. Common Pitfalls: Changing directions mid-derivation and breaking sign consistency. Final Answer: the directions are not critical

Question 3

2×2 determinant evaluation: The first row of a determinant is [10, 6] and the second row is [3, 5]. What is the value of this determinant (compute ad − bc)?

Accepted Answer

Introduction / Context: Determinants summarize key properties of matrices and are used in solving linear systems, computing inverses, and analyzing transformations. For 2×2 matrices, the determinant has a simple closed form: ad − bc. This question reinforces accurate arithmetic and sign handling for a basic case. Given Data / Assumptions: Matrix rows: [10, 6] and [3, 5]. Interpret as a 2×2 matrix [[10, 6], [3, 5]]. Use the standard 2×2 determinant formula. Concept / Approach: For a 2×2 matrix with entries a, b in the first row and c, d in the second row, the determinant value is ad − bc. Careful multiplication and subtraction yield the final scalar. Step-by-Step Solution: Let a = 10, b = 6, c = 3, d = 5.Compute products: ad = 10 * 5 = 50; bc = 6 * 3 = 18.Evaluate determinant: ad − bc = 50 − 18 = 32.Thus, the determinant equals 32. Verification / Alternative check: Cross-multiplication visualization: draw diagonals, product of the main diagonal minus product of the other diagonal. The arithmetic again gives 32, confirming the calculation. Why Other Options Are Wrong: 18 or 50: These are intermediate products, not the required difference. −32: Incorrect sign; ad − bc is positive for these values. Common Pitfalls: Reversing the subtraction order (bc − ad) and getting the wrong sign. Arithmetic slip in 6 * 3 or 10 * 5. Final Answer: 32

Question 4

Determinant techniques: The 'expansion' method for evaluating determinants is best described as which of the following?

Accepted Answer

Introduction / Context: Determinants can be computed with several techniques. For small matrices, manual expansion (such as Sarrus rule for 3×3, or cofactor expansion for 2×2 and 3×3) is straightforward and quick. For higher orders, systematic methods (row reduction, LU decomposition) are typically more efficient and less error-prone. Given Data / Assumptions: We compare the 'expansion' approach (manual expansion along rows/columns or Sarrus for 3×3) to other methods. Goal: identify the range where expansion is practically suitable. Concept / Approach: Cofactor/expansion methods scale poorly as order grows because the number of terms increases rapidly. However, for second- and third-order determinants, expansion is concise and transparent, making it a preferred hand-calculation technique in courses and exams. Step-by-Step Solution: For 2×2: determinant = ad − bc (a direct expansion).For 3×3: Sarrus rule or cofactor expansion works neatly with a manageable number of terms.For n ≥ 4: expansion becomes lengthy; algorithmic methods are favored. Verification / Alternative check: Compare operation counts: cofactor expansion grows combinatorially, whereas elimination (row-reduction to triangular form) uses polynomial-time operations, explaining why expansion is recommended mainly for low orders. Why Other Options Are Wrong: 'better than any other method': Not for high-order matrices. 'good for only one determinant': Nonsense; it applies to many but is manageable chiefly for small orders. 'more flexible than the cofactor method': Expansion is the cofactor method in essence for general determinants. Common Pitfalls: Applying expansion to large matrices and making arithmetic errors due to the explosion of terms. Final Answer: good for second- and third-order determinants

Question 5

Solve for I1 from the simultaneous linear equations 4I1 + 4I2 = 2 and 6I1 + 7I2 = 4 in the context of circuit analysis (report the correct sign and in amperes).

Accepted Answer

Introduction / Context: Systems of linear equations frequently arise from Kirchhoff's laws in electrical engineering. Here, I1 and I2 represent assumed branch or mesh currents. Solving the pair of equations correctly, including the sign, reveals the true direction of I1 relative to the assumed reference. Given Data / Assumptions: Equation 1: 4I1 + 4I2 = 2. Equation 2: 6I1 + 7I2 = 4. I1 and I2 are steady-state DC currents; units are amperes. Algebraic signs indicate direction with respect to the chosen current reference. Concept / Approach: Use substitution or elimination to solve two linear equations in two unknowns. The negative sign of a current solution means the real current flows opposite to the initially assumed direction—a common outcome in mesh/branch analyses. Step-by-Step Solution: From 4I1 + 4I2 = 2, isolate I1: I1 = (2 − 4I2) / 4 = 0.5 − I2.Substitute into 6I1 + 7I2 = 4: 6(0.5 − I2) + 7I2 = 4.Compute: 3 − 6I2 + 7I2 = 4 ⇒ 3 + I2 = 4 ⇒ I2 = 1 A.Back-substitute: I1 = 0.5 − 1 = −0.5 A. Verification / Alternative check: Plug (I1, I2) = (−0.5, 1) into both equations: 4(−0.5) + 4(1) = −2 + 4 = 2; 6(−0.5) + 7(1) = −3 + 7 = 4. Both hold, confirming the solution. Why Other Options Are Wrong: 0.5 A and 50 mA ignore the required negative sign and magnitude. −50 mA has the correct sign but is off by a factor of 10. Common Pitfalls: Dropping the negative sign, arithmetic slips while distributing coefficients, or failing to verify the solution in both equations. Final Answer: –0.5 A

Question 6

Solve for I2 from the pair of equations 4I1 + 4I2 = 2 and 6I1 + 7I2 = 4 (state the correct magnitude and sign in amperes).

Accepted Answer

Introduction / Context: When analyzing circuits using mesh or nodal methods, you often end up with simultaneous linear equations for unknown currents. Solving cleanly and confirming the sign ensures the physical interpretation (direction) is correct. Given Data / Assumptions: Equations: 4I1 + 4I2 = 2 and 6I1 + 7I2 = 4. Unknowns represent steady DC currents in amperes. Linear algebra methods (substitution/elimination) apply directly. Concept / Approach: Use substitution to isolate one variable and substitute into the other equation. Maintain unit consistency and sign discipline. The solution pair will satisfy both equations simultaneously. Step-by-Step Solution: From 4I1 + 4I2 = 2 ⇒ I1 = 0.5 − I2.Insert into 6I1 + 7I2 = 4: 6(0.5 − I2) + 7I2 = 4.Compute: 3 − 6I2 + 7I2 = 4 ⇒ 3 + I2 = 4 ⇒ I2 = 1 A.Therefore, I2 equals 1 ampere (positive relative to the assumed direction). Verification / Alternative check: Back-solve I1: I1 = 0.5 − 1 = −0.5 A. Check: 6(−0.5) + 7(1) = −3 + 7 = 4, confirming the solution pair (−0.5, 1). Why Other Options Are Wrong: −1 A has the wrong sign; 100 mA and −100 mA are an order of magnitude too small relative to the equation scaling. Common Pitfalls: Sign errors when combining like terms, rounding prematurely, or not validating against both original equations. Final Answer: 1 A

Question 7

Compute the value of a 2×2 determinant with first row [3, 5] and second row [7, 2]; use the formula det = ad − bc and select the correct result.

Accepted Answer

Introduction / Context: Determinants are fundamental in linear algebra and circuit analysis (for example, in Cramer's rule to solve mesh or node equations). A 2×2 determinant is simple to evaluate and provides insight into invertibility and orientation of linear transformations. Given Data / Assumptions: Matrix entries: first row (a, b) = (3, 5); second row (c, d) = (7, 2). All quantities are real numbers. Standard 2×2 determinant formula applies. Concept / Approach: For A = [[a, b], [c, d]], the determinant is computed as det(A) = ad − bc. The sign (positive or negative) indicates whether the associated linear mapping preserves or reverses orientation. Step-by-Step Solution: Identify terms: a = 3, b = 5, c = 7, d = 2.Apply formula: det = ad − bc.Multiply: ad = 32 = 6; bc = 57 = 35.Subtract: det = 6 − 35 = −29. Verification / Alternative check: Swap the two columns; the determinant would flip sign to +29. Since our column order is [3,5] and [7,2], the correct signed value is −29. Why Other Options Are Wrong: 31 and 39 arise from adding products instead of subtracting. −31 results from an arithmetic slip (e.g., using 32 = 4 or 57 = 36 mistakenly). Common Pitfalls: Reversing the subtraction order, sign mistakes, or mis-multiplying 5*7. Always compute ad and bc separately and then subtract. Final Answer: –29

Question 8

Equation count: In general practice, the mesh-current (loop) method produces fewer simultaneous equations than the node-voltage method. True or false?

Accepted Answer

Introduction / Context: Two cornerstone analysis techniques in circuit theory are the node-voltage (KCL-based) method and the mesh-current (KVL-based) method. Which one yields fewer equations depends on circuit topology; there is no universal rule favoring meshes over nodes. Given Data / Assumptions: Planar circuits are assumed for mesh analysis applicability. Node-voltage method requires N−1 equations for N nodes (with a chosen reference ground). Mesh-current method requires M equations for M meshes (independent loops). Concept / Approach: The relative sizes of N−1 and M determine which method is more compact. Many practical circuits have fewer essential nodes than meshes, making node-voltage equations fewer. Conversely, in some sparse planar layouts, M can be small. Hence, the blanket statement that mesh “generally” yields fewer equations is not reliable and is often false in modern network topologies. Step-by-Step Solution: Count essential nodes; compute N−1 KCL equations for node method.Count independent meshes; compute M KVL equations for mesh method.Compare N−1 versus M to choose the more efficient approach case-by-case. Verification / Alternative check: Example: a ladder with many series elements per rung often has relatively few nodes compared to the number of small loops, favoring node analysis. Simulation tools also often use nodal formulations internally, reflecting this efficiency. Why Other Options Are Wrong: Selecting “True” overlooks counterexamples where meshes greatly outnumber nodes. Common Pitfalls: Applying mesh analysis to non-planar circuits or circuits with many current sources, which complicates loop equations. Selecting the method should be dictated by topology, source types, and convenience. Final Answer: False

Question 9

Foundations of mesh analysis: The mesh-current method is fundamentally based on Kirchhoff’s Current Law (KCL). True or false?

Accepted Answer

Introduction / Context: Understanding which Kirchhoff law underpins each classical method helps you set up the right equations and avoid sign mistakes. Mesh analysis and node analysis complement each other but rest on different laws of circuit theory. Given Data / Assumptions: Mesh-current method writes loop equations around independent meshes. Kirchhoff’s Voltage Law (KVL) states the algebraic sum of voltages around a closed loop is zero. Kirchhoff’s Current Law (KCL) states the algebraic sum of currents at a node is zero. Concept / Approach: Mesh analysis assigns loop currents and applies KVL to each mesh. While KCL is still valid globally, it is not the primary law used to derive the mesh equations. Conversely, node-voltage analysis is directly based on KCL at each non-reference node. Step-by-Step Solution: Assign mesh currents to independent loops in a planar circuit.Write one KVL equation per mesh, summing drops across shared and unshared elements.Solve the resulting simultaneous equations for the mesh currents. Verification / Alternative check: Compare with node-voltage analysis: there, you would write ΣI_out = 0 at each node (KCL), not loop sums. This contrast confirms which law each method fundamentally uses. Why Other Options Are Wrong: Choosing “True” confuses the basis of the methods: mesh → KVL; node → KCL. Common Pitfalls: Attempting mesh analysis on non-planar circuits or with many current sources, which complicates forming loop equations. In such cases, node analysis (KCL-based) may be more straightforward. Final Answer: False

Question 10

Circuit analysis – Foundational concept check for the node-voltage (nodal) method Statement: “The node-voltage method is based on Kirchhoff’s voltage law (KVL).” Decide whether the statement is correct and choose the best option.

Accepted Answer

Introduction / Context: The node-voltage (nodal) method is one of the two cornerstone systematic techniques for linear circuit analysis, the other being the mesh-current method. Many learners mix up which Kirchhoff law underpins which technique. This question checks that foundational association. Given Data / Assumptions: We are analyzing linear lumped circuits using Kirchhoff’s laws. “Node-voltage method” refers to writing node equations in terms of node potentials relative to a common reference (ground). No special source or element types (e.g., dependent sources) are required for the basic statement under test. Concept / Approach: Kirchhoff’s current law (KCL) states that the algebraic sum of currents leaving/entering a node is zero. The node-voltage method writes one equation per essential node by summing currents (expressed via conductances/admittances and node voltages) to satisfy KCL. KVL is involved implicitly when expressing element currents by Ohm’s law using node-to-node voltage differences, but the governing equations are KCL equations at nodes. Step-by-Step Solution: 1) Select a reference node (ground).2) Assign unknown voltages to the remaining essential nodes.3) At each non-reference node, apply KCL: sum of currents leaving (or entering) equals zero.4) Express each current using element relationships, typically i = (Vnode − Vadjacent)/R or i = G * (Vnode − Vadjacent).5) Solve the simultaneous KCL equations for node voltages. Verification / Alternative check: Compare with the mesh-current method, which explicitly writes KVL around meshes. The clear division—nodal ↔ KCL; mesh ↔ KVL—confirms the statement is false. Why Other Options Are Wrong: “True” misattributes the primary law. “True only for single-loop circuits” and “Cannot be determined” add conditions that are irrelevant; the method’s foundation does not change with loop count or source type. Common Pitfalls: Assuming that because voltages are unknowns, the method must be “about KVL.” In reality, voltages are unknowns but the conservation law applied is KCL at each node. Final Answer: False.

Question 11

Linear algebra refresher – Evaluating a 2×2 determinant by cross-products Statement: “Second-order determinants are evaluated by subtracting the signed cross-products.”

Accepted Answer

Introduction / Context: Determinants are ubiquitous in circuit analysis (e.g., solving nodal equations via Cramer’s rule). Remembering how to compute a 2×2 determinant quickly is vital during timed exams and practical calculations. Given Data / Assumptions: A general 2×2 determinant is |a b; c d|. We are using standard determinant definitions (no special numeric assumptions). “Signed cross-products” refers to the conventional ad − bc ordering with sign. Concept / Approach: The value of a 2×2 determinant is computed as the product of the main diagonal minus the product of the off-diagonal: det = ad − bc. This is precisely “subtracting the signed cross-products.” The sign matters; reversing terms would flip the determinant’s sign and change solutions when used in linear systems. Step-by-Step Solution: Let the matrix be [[a, b], [c, d]].Compute main diagonal product: ad.Compute off-diagonal product: bc.Subtract: det = ad − bc. Verification / Alternative check: Check with a simple numeric example, e.g., [[2, 3], [1, 4]] gives det = 24 − 31 = 8 − 3 = 5, matching the rule. Why Other Options Are Wrong: “False,” “True only if diagonal entries are positive,” and “True only for symmetric matrices” introduce conditions that are irrelevant; the formula holds universally for 2×2 matrices. Common Pitfalls: Accidental sign reversal (writing bc − ad), or mixing the rule with Sarrus’ method (which is for 3×3 determinants, not 2×2). Final Answer: True.

Question 12

Assigning branch current directions – Do initial arrow choices matter? Statement: “When assigning branch currents, you need not be concerned with the direction you choose.”

Accepted Answer

Introduction / Context: Choosing current directions is the first step in writing KCL and KVL equations. Students often worry about “guessing wrong.” This item clarifies what happens if your initial choice differs from the actual physical current direction. Given Data / Assumptions: Linear lumped circuits analyzed with Kirchhoff’s laws. Currents are assigned with arbitrary reference directions for writing equations. Solutions can be positive or negative real numbers (or phasors). Concept / Approach: The reference direction is arbitrary. If the solved current value is positive, actual current flows in the assumed direction; if negative, the actual current flows opposite to the assumed arrow. The mathematics is consistent regardless of the initial choice. Therefore, you need not worry about “correctness” of the guess—only be consistent in equations. Step-by-Step Solution: 1) Draw the circuit and assign a current arrow for each branch.2) Write KCL at nodes and/or KVL around loops using the assigned arrows and passive sign convention.3) Solve the system; interpret signs of the solutions to infer actual directions. Verification / Alternative check: Try a simple series resistor example with a voltage source: assume current right-to-left; you will obtain a negative value, indicating left-to-right flow in reality, but the magnitude is correct. Why Other Options Are Wrong: “False” suggests the initial guess must match reality, which is untrue. The statements adding conditions (dc only, planar only) are irrelevant; the property is general across linear circuits. Common Pitfalls: Changing assumed directions mid-derivation, which breaks consistency; forgetting to flip voltage polarities when reversing current directions in element equations. Final Answer: True.

Question 13

Mesh/loop analysis – Is a loop current an actual branch current? Statement: “A loop current is an actual current in a branch.”

Accepted Answer

Introduction / Context: In mesh (loop) analysis, we introduce loop currents as mathematical variables to simplify KVL writing. It is important to distinguish these from the physical branch currents measured in components. Given Data / Assumptions: Loop currents are hypothetical variables assigned to each mesh. Branch current equals the algebraic sum of all loop currents passing through that branch, considering direction. No special source/element constraints are assumed. Concept / Approach: A loop current itself is not necessarily the actual branch current. Only in a branch that is exclusive to one loop does the branch current equal that loop current. In shared branches, the actual branch current equals the difference (or sum) of the relevant loop currents depending on assumed directions. Therefore, the blanket statement is false. Step-by-Step Solution: 1) Assign mesh currents I1, I2, … clockwise (convention).2) For a branch unique to mesh k, the branch current = Ik.3) For a branch common to meshes i and j, branch current = Ii − Ij (sign depends on chosen directions).4) Use these relations to compute physical currents after solving the mesh equations. Verification / Alternative check: Consider two meshes sharing a resistor. If I1 = 2 A and I2 = 0.5 A with opposing directions, the shared resistor’s branch current is 1.5 A in the direction of I1, not equal to either loop current alone. Why Other Options Are Wrong: “True” confuses variables with physical quantities. “True only in dc” is incorrect because the relationship holds for ac phasor analysis as well. “True only if the branch belongs to a single loop” is a conditional truth, but the original unconditional statement remains false. Common Pitfalls: Reporting mesh currents as branch currents without combining them in common branches; mixing up assumed directions leading to sign errors. Final Answer: False.

Question 14

Linear algebra refresher – Ways to evaluate a 3×3 determinant Statement: “Third-order determinants are evaluated by the expansion method or by the cofactor method.”

Accepted Answer

Introduction / Context: In circuit theory, 3×3 determinants appear when solving three simultaneous equations (e.g., three-node nodal analysis with Cramer’s rule). Knowing standard evaluation methods speeds up hand calculations and checks. Given Data / Assumptions: General 3×3 matrix with no special structure. Common textbook techniques include cofactor (Laplace) expansion and equivalent expansion by minors. Alternative mnemonics like Sarrus’ rule exist specifically for 3×3. Concept / Approach: “Expansion method” typically refers to expanding along a row or column using minors; the “cofactor method” is the same approach stated formally with signs (cofactors). Thus the statement is correct. One may also use Sarrus’ rule for 3×3, or convert to triangular form via elimination and multiply diagonal elements, but the assertion remains accurate as written. Step-by-Step Solution: 1) Choose a row/column with zeros if possible to reduce arithmetic.2) Compute minors by deleting the chosen row and column.3) Apply alternating signs to form cofactors.4) Sum the products of entries and their cofactors to obtain the determinant. Verification / Alternative check: Cross-verify with Sarrus’ shortcut for 3×3 matrices to ensure numerical consistency in practice. Why Other Options Are Wrong: “False” contradicts standard linear algebra. Claiming “only Gaussian elimination is valid” ignores many correct analytical methods. Common Pitfalls: Forgetting the checkerboard sign pattern of cofactors; arithmetic slips when computing minors; misapplying Sarrus to non-3×3 cases. Final Answer: True.

Question 15

Applicability of the mesh (loop-current) method Statement: “The mesh method can be applied to circuits with any number of loops.”

Accepted Answer

Introduction / Context: The mesh (loop-current) method is powerful but not universally applicable. Recognizing its domain of validity prevents wasted effort and mistakes when analyzing nonplanar networks or circuits with certain source placements. Given Data / Assumptions: Mesh analysis uses independent meshes (windows) of a planar circuit. Nonplanar circuits cannot be drawn without crossing branches; meshes are not well-defined. Current sources between two meshes can complicate writing KVL directly. Concept / Approach: Mesh analysis requires planarity. While the number of loops can be large, the method does not extend to nonplanar networks directly. Also, floating current sources between meshes necessitate supermesh handling or alternative formulations. Therefore, the unconditional statement “any number of loops” is false because topology, not just loop count, governs applicability. Step-by-Step Solution: 1) Check planarity (can the circuit be drawn without branch crossings?).2) Identify meshes; assign loop currents.3) If a current source lies between two meshes, form a supermesh and write constraint equations.4) If nonplanar, switch to nodal (KCL) or modified nodal analysis. Verification / Alternative check: Compare with nodal analysis, which is applicable to a broader set of circuits (including nonplanar), reinforcing that mesh is conditional. Why Other Options Are Wrong: “True” ignores topology limits. “True only if there are no current sources” is too restrictive because supermeshes handle many such cases. The best precise qualifier is “planar circuits,” captured by option C (but the statement under test, as written, is false). Common Pitfalls: Attempting mesh on bridge networks that are nonplanar in their electrical graph; forgetting to add current-source constraint equations. Final Answer: False.

Question 16

Branch-current (direct) method – Which Kirchhoff laws does it use? Statement: “The branch current method is based on Kirchhoff’s voltage law and Kirchhoff’s current law.”

Accepted Answer

Introduction / Context: The branch-current (direct) method writes unknowns as the actual currents in circuit branches and sets up equations using both Kirchhoff laws. Understanding this helps you choose between branch-current, nodal, and mesh methods for a given problem size and topology. Given Data / Assumptions: We have n branches with assigned current variables. We can form node equations (KCL) and loop equations (KVL) as needed to close the system. Ohm’s law links branch voltages and currents for passive elements. Concept / Approach: Branch-current analysis typically uses KCL at nodes to relate the unknown branch currents and KVL around independent loops to introduce element voltages and source effects. Thus both KCL and KVL are employed, unlike nodal (primarily KCL) or mesh (primarily KVL). Step-by-Step Solution: 1) Assign a current variable to each branch.2) Apply KCL at independent nodes to relate currents.3) Apply KVL around enough independent loops to include source voltages and element drops.4) Use element relations (e.g., v = R*i) to convert between voltages and currents. Verification / Alternative check: Counting equations vs. unknowns confirms that both node and loop constraints are needed unless special structures reduce the set. Why Other Options Are Wrong: “It uses only KCL” or “only KVL” understate the method; while some problems may be solvable with just one set of equations, the general branch-current framework relies on both laws. Common Pitfalls: Creating dependent equations (linear dependence) by choosing redundant KVL loops; forgetting reference polarities leading to sign errors. Final Answer: True.

Branch, Loop and Node Analyses Questions