Reciprocity Theorem Question & Answers May 29, 2023 By Wat Electrical This article lists 50 Reciprocity theorem MCQs for engineering students. All the Reciprocity theorem Questions & Answers given below include a hint and a link wherever possible to the relevant topic. This is helpful for users who are preparing for their exams, interviews, or professionals who would like to brush up on the fundamentals of Reciprocity theorem. The reciprocity theorem is a fundamental principle in physics and engineering that relates the behavior of a system to the interchangeability of sources and receivers. It states that the response at a point in a system due to a source is equal to the response at the same source due to a point. In other words, if we have two systems, System A and System B, and we interchange the positions of the source and receiver between the two systems while keeping all other conditions the same, the response observed in System A will be the same as the response observed in System B. The theorem is based on the principle of linearity and time-invariance of the system. It assumes that the system response is linear and remains unchanged over time. The reciprocity condition is satisfied when the sources are located at the same point in the two systems. The reciprocity theorem is applicable to various areas, including electromagnetism, acoustics, and structural mechanics. It has significant practical implications and is often used in engineering analysis and design. For example, in antenna design and analysis, the reciprocity theorem allows us to determine the radiation patterns and characteristics of an antenna by measuring the response at a nearby location instead of directly measuring the radiation. 1). Which theorem states that the response at a point due to a source is equal to the response at the same source due to a point? Biot-Savart's Law Ampere's Law Ohm's Law Reciprocity Theorem Hint 2). The reciprocity theorem is applicable to which of the following systems? Mechanical systems only Electrical systems only Magnetic systems only Mechanical, electrical, and magnetic systems Hint 3). According to the reciprocity theorem, the reciprocity condition is satisfied when ____________________? The response is linear and time-invariant The sources are located at the same point The sources and responses have the same frequency The responses are proportional to the sources Hint 4). In the context of electromagnetic fields, the reciprocity theorem is based on _____________________? Gauss's Law Faraday's Law Maxwell's Equations Coulomb's Law Hint 5). The reciprocity theorem finds applications in which of the following areas? Antenna design and analysis Structural mechanics Circuit analysis All of the above Hint 6). Which theorem relates the electric field produced by a charge distribution to the potential generated by another charge distribution? Gauss's law Ampere's law Faraday's law Reciprocity theorem Hint 7). According to the reciprocity theorem, if a charge distribution A produces a potential V at point P due to a unit charge at point Q, what will be the potential at point P if the unit charge is placed at point P and observed at point Q? V 2V V/2 V^2 Hint 8). The reciprocity theorem is applicable for which of the following scenarios? Static electric fields only Static magnetic fields only Both static electric and magnetic fields None of the above Hint 9). In the context of the reciprocity theorem, which of the following statements is true? The charge distributions A and B must be symmetrical. The charge distributions A and B must be identical. The charge distributions A and B must be in different locations. The charge distributions A and B can be arbitrary. Hint 10). The reciprocity theorem is based on the principle of ___________________? Conservation of charge Conservation of energy Conservation of momentum Conservation of electric field Hint 11). The reciprocity theorem is applicable to ______________________? Electrical circuits Mechanical systems Both electrical circuits and mechanical systems Neither electrical circuits nor mechanical systems Hint 12). The reciprocity theorem is based on the principle of ____________________? Conservation of energy Conservation of momentum Conservation of charge Conservation of power Hint 13). The reciprocity theorem is often used to analyze ___________________? Power systems Transmissions lines Antennas All of the above Hint 14). The mathematical expression of the reciprocity theorem in electrical circuits is: V1/I2 = V2/I1 V1/I1 = V2/I2 V1/V2 = I1/I2 V1/I1 = I2/V Hint 15). The reciprocity theorem is not valid for ____________________? Linear systems Time-invariant systems Reciprocal systems None of the above Hint Reciprocity Theorem MCQ for Exams 16). The reciprocity theorem is applicable to which type of circuits? Resistive circuits Inductive circuits Capacitive circuits All of the above Hint 17). The reciprocity theorem relates to the interchangeability of which two circuit parameters? Voltage and current Resistance and reactance Power and energy Impedance and admittance Hint 18). In the context of the reciprocity theorem, the ratio of currents or voltages is called ________________? Reciprocal ratio Symmetry ratio Transfer ratio Reciprocity factor Hint 19). The reciprocity theorem holds true for which type of linear circuits? Time-invariant circuits Nonlinear circuits Time-varying circuits Passive circuits Hint 20). Which of the following statements is true regarding the advantages of the reciprocity theorem? It simplifies the analysis of complex circuits. It reduces the number of circuit variables to be solved. It provides a powerful tool for circuit design and optimization. All of the above. Hint 21). In a circuit, a current of 2 A flowing from terminal A to terminal B results in a voltage of 4 V across terminals C and D. What will be the voltage across terminals A and B if a current of 3 A flows from C to D? 6 V 8 V 12 V 16 V Hint 22). In a circuit, a voltage of 10 V applied across terminals X and Y results in a current of 2 A flowing from terminal Z to terminal W. What will be the current flowing from X to Y if a voltage of 5 V is applied across terminals Z and W? 0.5 A 1 A 2 A 4 A Hint 23). In a circuit, a voltage of 6 V applied across terminals P and Q results in a current of 3 A flowing from terminal R to terminal S. If the voltage across terminals R and S is 9 V, what will be the current flowing from P to Q? 1 A 2 A 3 A 4 A Hint 24). In a circuit, a current of 5 A flowing from terminal A to terminal B results in a power dissipation of 50 W. What will be the power dissipation if a current of 3 A flows from B to A? 30 W 50 W 90 W 150 W Hint 25). Consider two circuits, Circuit A and Circuit B. If a current of 2A flows through Circuit A when a voltage of 4V is applied across its terminals, what will be the voltage across the terminals of Circuit B when a current of 3A flows through it? 1.5V 2V 4.5V 6V Hint 26). A voltage of 10V applied across terminals A and B of Circuit A produces a current of 5A. If the same voltage source is now applied across terminals X and Y of Circuit B, what will be the current flowing through Circuit B? 2A 5A 10A 25A Hint 27). Reciprocity in electromagnetic systems refers to ____________________? The equality of forward and backward scattering coefficients The interchangeability of transmitting and receiving antennas The symmetry of the transmission line impedance. The equality of forward and backward voltage waves Hint 28). Reciprocity in acoustic systems refers to __________________? The equality of sound absorption coefficients The symmetry of sound wave propagation The interchangeability of microphones and speakers The equality of sound pressure levels Hint 29). Reciprocity in circuit theory refers to __________________? The equality of input and output impedances The symmetry of current and voltage waveforms The interchangeability of resistors and capacitors. The equality of forward and backward voltage waves. Hint 30). Reciprocity in optical systems refers to __________________? The symmetry of light propagation The equality of absorption and emission spectra The interchangeability of lenses and mirrors The equality of forward and backward light intensities Hint 31). Reciprocity in thermal systems refers to __________________? The equality of thermal conductivity and thermal resistance The interchangeability of heating and cooling elements The symmetry of temperature distribution The equality of forward and backward heat fluxes Hint 32). One of the disadvantages of the reciprocity theorem is ? It only applies to linear circuits It cannot be used for AC circuits It is difficult to apply in practical circuit analysis It requires complex mathematical calculations Hint 33). The reciprocity theorem may not hold true in circuits with ____________________? Ideal resistors only Reactive elements Nonlinear elements Ideal voltage sources only Hint 34). The reciprocity theorem does not consider the effects of ______________________? Capacitance in the circuit Inductance in the circuit Mutual inductance and capacitance Resistance in the circuit Hint 35). The reciprocity theorem may not be applicable in circuits with _____________________? Time-varying parameters Ideal current sources Passive elements only Balanced configurations Hint Reciprocity Theorem MCQ for Interviews 36). One of the disadvantages of the reciprocity theorem is that it ___________________? Requires complex circuit simulations Only applies to circuits with ideal components Cannot be used for circuit optimization May not hold true in circuits with active components Hint 37). Which of the following statements best describes the Lorentz Reciprocity Theorem? It states that the magnetic field induced by an electric current is perpendicular to the direction of current flow. It states that the electric field induced by a magnetic field is proportional to the rate of change of the magnetic field. It states that the electric field induced by a magnetic field is proportional to the rate of change of the magnetic field. Hint 38). According to the Lorentz Reciprocity Theorem, which of the following conditions must be satisfied for two circuits to exhibit reciprocity? The circuits must have the same resistance. The circuits must have the same inductance The circuits must have the same capacitance. The circuits must be linear, time-invariant, and reciprocal. Hint 39). In the context of electromagnetic waves, the Lorentz Reciprocity Theorem implies that _____________________? The speed of light is constant in all inertial frames of reference The intensity of an electromagnetic wave is inversely proportional to the square of the distance from the source. The direction of propagation of an electromagnetic wave is always perpendicular to the electric and magnetic fields The transmission and reflection coefficients of an electromagnetic wave are the same when the roles of the source and receiver are interchanged. Hint 40). Which of the following applications is NOT related to the Lorentz Reciprocity Theorem? Antenna design and analysis. Electrical circuit modeling and analysis Optical waveguide design and analysis Fluid dynamics and flow analysis Hint 41). In the context of three-dimensional finite element analysis, the stiffness matrix for an element with linear shape functions and constant material properties has dimensions of _____________________? 2x2 3x3 4x4 6x6 Hint 42). The formulation of three-dimensional finite elements typically involves the discretization of the domain into ____________________? Lines Triangles Quadrilaterals Tetrahedral Hint 43). In three-dimensional finite element analysis, the interpolation of the field variable within an element is typically performed using ________________________? Lagrange polynomials Hermite polynomials B-splines Bernstein polynomials Hint 44). The three-dimensional stress-strain relationship for linear elastic materials is given by __________________? Hooke’s law Navier’s law Euler’s law Cauchy’s law Hint 45). In three-dimensional finite element analysis, the element stiffness matrix is obtained by ______________________? Numerical integration Analytical integration Closed-form solution Direct matrix inversion Hint 46). In the context of two-dimensional plane-strain analysis, the strain components that are assumed to be zero are _________________? εxx and εyy εxy and εxz εyz and εzz εyz and εzx Hint 47). The equilibrium equations for two-dimensional plane-strain analysis are expressed as _________________? ∂σxx/∂x + ∂σxy/∂y + ∂σxz/∂z = 0 ∂σxx/∂x + ∂σxy/∂y + ∂σyz/∂z = 0 ∂σxx/∂x + ∂σyy/∂y + ∂σxy/∂z = 0 ∂σxx/∂x + ∂σxy/∂y + ∂σzz/∂z = 0 Hint 48). The constitutive relationship for linear elastic materials in two-dimensional plane-strain analysis is given by ________________? Hooke’s law Navier’s law Euler’s law Cauchy’s law Hint 49). The strain-displacement relations in two-dimensional plane-strain analysis are expressed as _______________? εxx = ∂u/∂x, εyy = ∂v/∂y, εxy = (∂u/∂y + ∂v/∂x), εzz = 0 εxx = ∂u/∂x, εyy = ∂v/∂y, εxy = (∂u/∂y + ∂v/∂x), εzz = ∂w/∂z εxx = ∂u/∂x, εyy = ∂v/∂y, εxy = (∂u/∂x + ∂v/∂y), εzz = 0 Hint 50). The plane-strain assumption is suitable for analyzing ________________________? Thick structures Axisymmetric structures Structures subjected to shear loading Thin structures with negligible out-of-plane deformation Hint Time's up
