Inductance
Introduced| English |
|---|
| inductance/ɪnˈdʌktəns/ |
| henries/ˈhenriz/ |
A coil resists changes to its own current — electrical inertia
- Try to switch a coil's current on suddenly and it fights back.
- Its own changing flux induces an EMF that opposes the change.
- This self-opposition is called inductance 电感.
- Think of it as electrical inertia: current in a coil doesn't like to change quickly.
The self-induced EMF
- A changing current makes a changing flux through the coil's own turns.
- By Faraday and Lenz, this induces a back-EMF: $\varepsilon = -L\dfrac{dI}{dt}$.
- $L$ is the inductance, measured in henries 亨利 (H).
- The faster you change the current, the harder the coil pushes back.
The self-induced EMF of an inductor is:
$\varepsilon = -L\,dI/dt$ — proportional to the rate of current change.
A $4\ \text{H}$ inductor's current changes at $2\ \text{A/s}$. Find the induced EMF magnitude (in V).
$|\varepsilon| = L\,dI/dt = 4 \times 2 = 8\ \text{V}$.
The SI unit of inductance is the ____.
Inductance $L$ is measured in henries (H).
What sets the inductance
- Like capacitance, $L$ depends on geometry, not on the current.
- More turns, a bigger area, or a longer coil change $L$.
- A tightly wound solenoid with many turns has a large inductance.
- Add an iron core and $L$ grows much larger still.
Energy stored in the field
- Building up a current stores energy in the coil's magnetic field.
- The stored energy is $U = \tfrac12 L I^2$.
- Compare it with a capacitor's $\tfrac12 C V^2$ — the magnetic twin.
- Switch the current off suddenly and this energy has to go somewhere (often a spark).
Inductance opposes change
A changing current in a coil induces a back-EMF proportional to how fast the current changes.
The energy stored in an inductor carrying current $I$ is:
$U = \tfrac12 LI^2$ — the magnetic twin of $\tfrac12 CV^2$.
The mirror image of a capacitor
- A capacitor opposes sudden changes in voltage.
- An inductor opposes sudden changes in current.
- A capacitor stores energy in an electric field; an inductor in a magnetic field.
- Together they are the two energy-storing circuit elements.
With a steady, unchanging current, an ideal inductor behaves like an ordinary wire.
$dI/dt = 0$ gives zero back-EMF, so it acts like a plain wire.
Select all true statements about an inductor.
Opposes current change, stores ½LI², geometric L. Opposing voltage change is a capacitor.
A coil has $L = 2\ \text{H}$ and its current changes at $3\ \text{A/s}$. Find the induced EMF.
- $|\varepsilon| = L\dfrac{dI}{dt} = 2 \times 3$.
- $|\varepsilon| = 6\ \text{V}$, opposing the change.
An inductor opposes a change in current, not the current itself. A steady current ($dI/dt = 0$) induces no back-EMF at all — the coil then behaves like an ordinary wire. It only fights while the current is changing.
Inductance $L$ (in henries) is a coil's electrical inertia: a changing current self-induces a back-EMF $\varepsilon = -L\,dI/dt$. It depends on geometry and stores energy $U = \tfrac12 LI^2$. An inductor opposes changes in current, the mirror of a capacitor opposing changes in voltage.