Network Theorems MCQ [Free PDF] – 8 Objective Questions with Answers

If a circuit response x depends linearly on independent sources u₁, u₂, …, then x(u₁+u₂+…) = x(u₁)+x(u₂)+…. Controlled/dependent sources stay in the circuit because their value is tied to another circuit variable; turning them off changes the network itself and destroys the correct controlling relationship.

Exam focus: When applying superposition, write “independent OFF, dependent ON” before starting the circuit reduction. Common trap: A very common error is to short/open a dependent source or to add individual source powers.

Superposition is a linear-circuit method used to find voltages or currents caused by multiple independent sources. Analyze one independent source at a time, replace other independent voltage sources by shorts and independent current sources by opens, and keep dependent sources active. Key relation: x = x₁ + x₂ + … for a linear response; P = V²/R = I²R is not a superposable quantity.

Exam focus: Deactivate only independent sources; never suppress a dependent source. Common trap: Adding powers from separate source cases is a classic trap.

The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.

Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. For a network with independent sources, Rth/Zth is found by suppressing independent sources; dependent sources remain and may require a test-source method. Key relation: V_th=V_OC; Z_th seen at the port with independent sources suppressed.

Exam focus: In AC, use impedances—not just resistances. Common trap: Dependent sources are not turned off when finding Thevenin resistance.

B — Thevenin's theorem: V_th (open-circuit voltage) in series with R_th. Norton's theorem uses a current source in parallel instead.

A — Only linear, bilateral AC and DC circuits. Thevenin's theorem replaces a linear two-terminal network by an equivalent voltage source with a series resistance/impedance.

In AC, ZL must equal the complex conjugate of source/Thevenin impedance. At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%. Key relation: DC: R_L=R_th. AC: Z_L=Z_th*.

Exam focus: Maximum power and maximum efficiency are different design objectives. Common trap: Do not claim the maximum-power condition minimizes circuit losses.

Source transformation preserves the terminal voltage-current behavior of a linear source-resistance pair. A voltage source Vs in series with R is equivalent to a current source Is=Vs/R in parallel with the same R, and conversely Vs=IsR. Key relation: Vs = Is R; Is = Vs/R.

Exam focus: Keep the resistance value unchanged when converting the source form. Common trap: Do not place the transformed resistor in the wrong series/parallel position.