ENGINEERING CIRCUIT ANALYSIS
CERTIFICATION PAPER 2026 FULL
SOLUTION GRADED A+
● Core Laws: Write the standard KCL equation at a node. Answer: Σ
i_k = 0 (with a consistent sign convention for currents at the node).
● Core Laws: What does Kirchhoff's Voltage Law (KVL) state?
Answer: The algebraic sum of voltages around any closed loop is zero.
● Core Laws: Write the standard KVL equation around a loop. Answer:
Σ v_k = 0 (with a consistent sign convention around the loop).
● Core Laws: What is the passive sign convention? Answer: If current
enters the labeled positive terminal of an element, the element's power is
positive when it absorbs power (p = +vi).
● Core Laws: What is the power equation using the passive sign
convention? Answer: p = v i (positive means absorbed if current enters
the + terminal).
● Core Laws: What does a positive power value mean with the passive
sign convention? Answer: The element is absorbing power.
, ● Core Laws: What does a negative power value mean with the passive
sign convention? Answer: The element is delivering power to the circuit.
● Core Laws: State Ohm's Law (time domain). Answer: v(t) = R i(t)
● Core Laws: State Ohm's Law (phasor domain for AC steady state).
Answer: V = R I
● Core Laws: What is the defining relationship for a capacitor in the
time domain? Answer: i(t) = C dv(t)/dt
● Core Laws: What is the defining relationship for an inductor in the
time domain? Answer: v(t) = L di(t)/dt
● Core Laws: In DC steady state, what is the capacitor equivalent?
Answer: Open circuit (no steady state DC current through an ideal
capacitor).
● Core Laws: In DC steady state, what is the inductor equivalent?
Answer: Short circuit (no steady state DC voltage across an ideal
inductor).
● Core Laws: In AC steady state, what mathematical tool is commonly
used to simplify sinusoidal analysis? Answer: Phasors and complex
impedance.
CERTIFICATION PAPER 2026 FULL
SOLUTION GRADED A+
● Core Laws: Write the standard KCL equation at a node. Answer: Σ
i_k = 0 (with a consistent sign convention for currents at the node).
● Core Laws: What does Kirchhoff's Voltage Law (KVL) state?
Answer: The algebraic sum of voltages around any closed loop is zero.
● Core Laws: Write the standard KVL equation around a loop. Answer:
Σ v_k = 0 (with a consistent sign convention around the loop).
● Core Laws: What is the passive sign convention? Answer: If current
enters the labeled positive terminal of an element, the element's power is
positive when it absorbs power (p = +vi).
● Core Laws: What is the power equation using the passive sign
convention? Answer: p = v i (positive means absorbed if current enters
the + terminal).
● Core Laws: What does a positive power value mean with the passive
sign convention? Answer: The element is absorbing power.
, ● Core Laws: What does a negative power value mean with the passive
sign convention? Answer: The element is delivering power to the circuit.
● Core Laws: State Ohm's Law (time domain). Answer: v(t) = R i(t)
● Core Laws: State Ohm's Law (phasor domain for AC steady state).
Answer: V = R I
● Core Laws: What is the defining relationship for a capacitor in the
time domain? Answer: i(t) = C dv(t)/dt
● Core Laws: What is the defining relationship for an inductor in the
time domain? Answer: v(t) = L di(t)/dt
● Core Laws: In DC steady state, what is the capacitor equivalent?
Answer: Open circuit (no steady state DC current through an ideal
capacitor).
● Core Laws: In DC steady state, what is the inductor equivalent?
Answer: Short circuit (no steady state DC voltage across an ideal
inductor).
● Core Laws: In AC steady state, what mathematical tool is commonly
used to simplify sinusoidal analysis? Answer: Phasors and complex
impedance.
