Questions: Capacitors and Inductors as Energy Storage Elements
3 questions to test your understanding
Score: 0 / 3
Question 1 Multiple Choice
Capacitors and inductors follow a duality principle for series/parallel combinations. Which statement correctly describes this duality?
ACapacitors in series combine like resistors in series; inductors in parallel combine like resistors in parallel.
BCapacitors in series combine like resistors in parallel; inductors in parallel combine like resistors in series.
CCapacitors in parallel combine like resistors in parallel; inductors in series combine like resistors in series.
DCapacitors and inductors both follow the same series/parallel rules as resistors.
The duality flips the rules: capacitors in series add reciprocals (1/C_total = 1/C1 + 1/C2), just as resistors in parallel do, while capacitors in parallel add directly. Inductors in series add directly (like resistors in series) and in parallel add reciprocals. This duality arises because C and L play symmetric roles when you swap voltage and current.
Question 2 True / False
A capacitor's voltage can change instantaneously if a large enough current pulse is applied.
TTrue
FFalse
Answer: False
The capacitor's i-v relationship is i = C(dv/dt). An instantaneous voltage change would require dv/dt → ∞, which demands infinite current. No physical source can supply infinite current, so capacitor voltage cannot change instantaneously. The same logic applies dually to inductor current: v = L(di/dt) means instantaneous current change would require infinite voltage.
Question 3 Short Answer
At the moment a switch closes in a circuit containing an inductor, why is the inductor current treated as a known initial condition rather than solved as an unknown?
Think about your answer, then reveal below.
Model answer: Inductor current cannot change instantaneously because an instantaneous change would require infinite voltage (v = L·di/dt). Therefore the current immediately after switching equals the current immediately before switching. This continuity constraint sets the initial condition that the transient solution must satisfy.
Energy stored in the inductor's magnetic field is E = ½LI². For this energy to change instantaneously, an infinite power would be required, which is physically impossible. The initial current value anchors the solution to the differential equation governing the circuit's transient response.