A circuit contains two independent voltage sources and one dependent current source. When applying superposition, how many sub-circuits do you analyze, and how is the dependent source treated?
AThree sub-circuits — one per source, including the dependent source, which is deactivated in the other two
BTwo sub-circuits — one per independent source; the dependent source is deactivated in each
CTwo sub-circuits — one per independent source; the dependent source remains active in both
DOne sub-circuit — superposition only applies when all sources are independent
Superposition deactivates independent sources one at a time — here, two sub-circuits. The dependent source is never deactivated because it models a real physical coupling (its output is controlled by a circuit variable). Deactivating it would eliminate the gain mechanism it represents, giving wrong answers. Option B is the most tempting wrong answer: it correctly counts two sub-circuits but incorrectly treats the dependent source like an independent one.
Question 2 Multiple Choice
Applying superposition, you find that source A contributes 3 W to a resistor and source B contributes 4 W. What is the total power dissipated by the resistor?
A7 W — power contributions add just like voltage and current contributions
B1 W — the contributions partially cancel
CCannot be determined from this information; total power must be computed from the combined voltage or current after superposition
D25 W — power adds in quadrature (3² + 4² = 25)
Power is P = V²/R — a nonlinear (quadratic) function of voltage. Superposition only applies to linear quantities (voltages and currents). The total power is (V_A + V_B)²/R = V_A²/R + 2V_A·V_B/R + V_B²/R, which includes a cross-term 2V_A·V_B/R that vanishes only when the contributions are orthogonal. To find total power, compute the combined voltage (or current) first, then calculate power from that combined quantity.
Question 3 True / False
When applying superposition, dependent sources should be deactivated (set to zero) in each sub-circuit, just like independent sources.
TTrue
FFalse
Answer: False
Only independent sources are deactivated. Dependent sources model physical couplings — transistor gain, op-amp behavior — whose output depends on a circuit variable. Deactivating them would remove the coupling entirely and produce incorrect results. The rule is: independent sources go off one at a time; dependent sources stay on always.
Question 4 True / False
Superposition can be used to calculate the total voltage across any element in a linear circuit with multiple independent sources.
TTrue
FFalse
Answer: True
Kirchhoff's voltage and current laws are linear equations in voltages and currents. Linearity means responses from independent sources add without interaction (for voltages and currents). So the total voltage across any element equals the algebraic sum of the contributions from each source acting alone — this is exactly what superposition states. The key constraint is linearity: superposition only applies to linear circuits.
Question 5 Short Answer
Why does superposition apply to voltages and currents in a linear circuit, but not to power dissipation?
Think about your answer, then reveal below.
Model answer: Superposition follows from linearity: KVL and KCL are linear equations, so solutions from multiple sources add independently. Power, however, is P = V²/R — a quadratic (nonlinear) function of voltage. Squaring a sum introduces cross-terms: (V₁ + V₂)²/R = V₁²/R + 2V₁V₂/R + V₂²/R. The cross-term 2V₁V₂/R is missed if you add the individual powers, making the sum incorrect. Total power must always be computed from the combined voltage or current after superposition, never by summing partial powers.
A practical consequence: in amplifier analysis, you can superpose the signal component and the DC bias to find total voltages and currents. But to find total power dissipated (e.g., for thermal design), you must use the combined waveform — which includes the signal-bias interaction term that superposing powers would miss.