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1.1.12 · D5Electricity & Charge Basics

Question bank — Understand inductance and the henry

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Figure — Understand inductance and the henry
Figure — Understand inductance and the henry
Figure — Understand inductance and the henry

True or false — justify

An ideal inductor carrying a steady 5 A DC current has 5 V across it.
False. Voltage obeys ; steady current means , so . The inductor is just a wire in steady DC no matter how big the current.
Doubling the current through a coil doubles its inductance.
False. but , so the ratio is fixed by geometry — the cancels. does not depend on current at all (for a linear, non-saturating core).
Doubling the number of turns doubles the inductance.
False. , so doubling makes it 4×. More turns raise both the field strength and the number of loops that link it, so the effect squares (see Figure s02).
An inductor stores energy in the electric field between its wires.
False. It stores energy in the magnetic field wrapped around the current: . Electric-field storage is the capacitor's job ().
The minus sign in means an inductor destroys energy.
False. The minus sign is direction (Lenz's law — EMF opposes the change), not loss. An ideal inductor stores and returns energy; it dissipates nothing.
A 1 H inductor and a 1 F capacitor store energy by the same mechanism.
False. They are duals: the inductor resists current change (magnetic field), the capacitor resists voltage change (electric field). Same "energy-storing passive" family, opposite quantities.
If you open a switch on a current-carrying inductor, the current stops instantly.
False. The inductor fights any sudden ; forcing current to zero fast makes huge, so spikes to a large voltage — that's the spark or arc across the switch.
Inductance is measured in webers.
False. Flux is in webers; inductance is in henries, where . Inductance is flux linkage per amp, so you divide out the current.
An air-core coil and an identical iron-core coil have the same inductance.
False. and iron has a far larger permeability , so the iron core gives dramatically more for the same turns and size.
A resistor and an ideal inductor both drop voltage in proportion to the current.
False. The resistor does (), but the inductor's voltage tracks the rate of change , not . Constant current → resistor still drops voltage, inductor drops none.
Under AC drive, the peak inductor voltage and peak current happen at the same instant.
False. For , — a cosine, which peaks a quarter-cycle before the current. Voltage leads current by in an ideal inductor.

Spot the error

"Since , a bigger current always means a bigger inductor voltage."
The error is confusing with . Voltage depends on how fast the current changes; a huge steady current gives zero voltage, while a tiny but rapidly changing current can give a large one.
", so if the current is negative the stored energy is negative."
The error ignores the square: always, so energy is always . Reversing current direction stores the same energy — the field just points the other way.
"An inductor with 0 A through it stores J, so it can never give a spark."
The error is a snapshot fallacy. With there's no stored energy, but a changing current from a nonzero value produces the spike. The spark comes from the current that was flowing, interrupted quickly.
", so a longer solenoid always has more inductance."
The error: for a fixed number of turns , sits in the denominator, so stretching those same turns over a greater length lowers — the field weakens as the loops spread apart. Only more turns per length raises it.
"Faraday gives ; since is constant we can't get any voltage."
The error confuses being constant with being constant. , and changes with time, so — a constant still gives voltage whenever the current moves.
"Two identical coils placed side by side each store , so total is exactly ."
The error ignores that nearby coils share flux (mutual coupling), so the total inductance and stored energy differ from simply adding — the fields interact.
"An inductor blocks AC just like a resistor blocks current, so we can quote a fixed ohm value for it."
The error is treating it as frequency-independent. Its opposition is the reactance , which grows with frequency — high-frequency current is opposed far more than low-frequency current, unlike a fixed resistor.

Why questions

Why does the inductor's voltage depend on and not on ?
Because voltage comes from changing flux (Faraday's law), and flux ; only a changing changes the flux, so only produces EMF.
Why is the henry defined using a rate (1 A/s → 1 V) rather than a static amount?
Because inductance governs opposition to change; the only meaningful measurable is how much voltage a given rate of current change produces, which is exactly .
Why does scale with instead of ?
One factor of because more turns make a stronger field (), a second factor because that flux links all turns. Field strength × turns-linked = (see Figure s02).
Why can an inductor produce a voltage far larger than the source that drove its current?
When current is interrupted, becomes enormous over a tiny time; can then far exceed the original supply — this is how ignition coils and boost converters make high voltages.
Why does an inductor behave like a "short circuit" long after being connected to DC?
Once current has settled to its steady value, , so . Zero volts across it means it looks like a plain wire (an ideal short) in the final state.
Why does an inductor oppose high-frequency AC more than low-frequency AC?
Its reactance is ; higher frequency means the current reverses faster, so is larger and is larger — more opposition for the same current amplitude.
Why is the inductor called the "dual" of the capacitor?
Swap voltage↔current and electric↔magnetic: a capacitor holds voltage and resists its change; an inductor holds current and resists its change. The equations mirror each other (, ).

Edge cases

What is the voltage across an ideal inductor at the exact instant a constant current has just been reached?
Zero. At steady state , so , even though a large current may be flowing.
What happens to if the core saturates (iron can't magnetise further)?
Effective drops sharply, so falls — the coil suddenly stores far less flux per amp and behaves more like an air core. This breaks the "L is constant" assumption.
Is ever negative or zero for a real single coil?
No. Geometry gives ; a coil always opposes change in one consistent sense. (Mutual inductance between coils can be signed, but self-inductance is positive.)
What does approach as the number of turns goes to zero (a straight wire)?
from ; a single short straight wire has tiny inductance because almost no flux is linked. The "coil" behaviour needs many linked turns.
If two identical inductors are connected in series (no coupling), what is the total inductance?
They add: . Same current flows through both and their flux linkages sum, just like resistors in series.
If two identical inductors are connected in parallel (no coupling), what is the total?
They combine like resistors in parallel: . The current splits, so each links less flux for the shared voltage.
At the very first instant you connect an inductor to a battery through a resistor, what is the current?
Zero. The inductor opposes any sudden jump, forcing initially; current then rises smoothly toward its steady value — see RL Circuits and Time Constant.
In the DC limit (frequency ), what happens to the inductor's reactance ?
It goes to zero — an inductor offers no opposition to DC once steady, consistent with it looking like a plain wire. Reactance only appears when the current is changing.

Connections