A circuit contains a large inductor carrying steady current. A switch is suddenly opened, interrupting the current path. What happens immediately after the switch opens?
ACurrent stops instantly because the switch breaks the circuit
BThe inductor drives current through whatever path is available, potentially generating a large voltage spike
CThe magnetic field immediately collapses with no further effect on the circuit
DThe inductor stores extra charge in its windings, which discharges slowly through the switch contacts
An inductor resists changes to current — it will generate whatever back-EMF is necessary to maintain that current through any available path. When the switch opens, if no low-resistance path exists, the inductor generates a large voltage spike to push current through the switch gap or any parasitic path. The stored magnetic energy is real and must go somewhere; it does not simply disappear. This is why circuits with large inductors require flyback diodes or snubbers. Option A reflects the naive misconception that a broken circuit instantly stops all current.
Question 2 Multiple Choice
The number of turns in a solenoid is doubled while keeping its length and cross-sectional area the same. What happens to its self-inductance?
AIt doubles, because twice as many turns means twice the inductance
BIt quadruples, because L = μ₀N²A/ℓ and N appears squared
CIt stays the same, because the geometry (length and area) is unchanged
DIt halves, because the wire is now twice as densely wound and the field concentrates differently
L = μ₀N²A/ℓ. Doubling N gives L → μ₀(2N)²A/ℓ = 4μ₀N²A/ℓ — four times the original. The N² dependence means inductance is very sensitive to turns: each turn contributes both more flux and more flux linkage with all other turns. Option A (linear dependence) is the most common error, assuming a simple proportional relationship without noticing the exponent.
Question 3 True / False
A self-induced EMF resists any current flowing through an inductor, meaning inductors usually oppose current.
TTrue
FFalse
Answer: False
Self-inductance opposes changes in current, not current itself. A steady current flowing through an ideal inductor produces no self-induced EMF at all — dI/dt = 0, so ε = −L(dI/dt) = 0. The inductor only generates a back-EMF when you try to increase or decrease the current. This is the electromagnetic analogue of inertia: a massive object at constant velocity requires no force to maintain it, and an inductor at constant current requires no back-EMF. Confusing 'opposes changes in current' with 'opposes current' is the central misconception.
Question 4 True / False
The energy stored in an inductor is proportional to the square of the current flowing through it.
TTrue
FFalse
Answer: True
U = (1/2)LI². Doubling the current quadruples the stored energy. This parallels the energy stored in a capacitor (½CV²) and kinetic energy (½mv²) — all quadratic in the relevant 'flow' quantity. The squared dependence means small currents store little energy, but energy grows rapidly with current, which is why high-current inductors in power supplies store significant energy and require careful circuit protection when interrupted.
Question 5 Short Answer
In what sense is an inductor the electromagnetic analogue of a massive object, and why does this analogy correctly predict an inductor's behavior when current is interrupted?
Think about your answer, then reveal below.
Model answer: Both mass and inductance resist changes to their respective flows: mass resists velocity changes (F = m·dv/dt) while inductance resists current changes (ε = L·dI/dt). Just as a massive moving object tends to continue moving and exerts large impulsive forces if abruptly stopped, an inductor carrying current tends to maintain that current and generates large voltage spikes if the current is suddenly interrupted. In both cases, stored energy (½mv² and ½LI²) must be dissipated or transferred — it cannot simply vanish.
The analogy extends to energy storage and the ODE structure: the RLC circuit and the spring-mass system are formally equivalent, with L ↔ m (inertia), R ↔ c (damping), and 1/C ↔ k (restoring force). Understanding inductance as electromagnetic inertia correctly predicts all its behaviors — why it takes time to build current, why it opposes rapid changes, and why interrupting it without a discharge path causes dangerous voltage spikes.