Inductance

Also called Self-inductance

The tendency of a conductor to oppose a change in the electric current through it, measured in henries. A circuit element built to have a large inductance is an inductor, usually a coil.

AP Physics C: Electricity and Magnetism, topic 13.4. The CED's definition is exactly that sentence: inductance is the tendency of a conductor to oppose a change in electrical current. Straight wires are modelled as having zero inductance; an inductor, such as a solenoid, is a circuit element with a significant amount of it.

Three printed relations:

E=−LdIdtLsol=μcoreN2AℓUL=12LI2\mathcal{E} = -L\frac{dI}{dt} \qquad L_{\text{sol}} = \frac{\mu_{\text{core}} N^2 A}{\ell} \qquad U_L = \tfrac{1}{2}LI^2

The first says the induced emf answers to the rate of change of current, not to the current. A steady current through an ideal inductor produces no emf at all. The second squares the total turn count NN, not the turns per unit length. The third is energy stored in the magnetic field, and it is the reason an inductor cannot change its current instantly: that would demand infinite power.

The two limits are what exam questions turn on.

  • At the instant a switch is thrown, the induced emf matches and opposes the applied potential difference across that branch, so the current through the inductor is still zero and it behaves as a break in the circuit.
  • After a time much longer than τ=L/R\tau = L/R, the CED says an inductor behaves as a conducting wire with zero resistance. The current has stopped changing, so there is nothing left to oppose.

Those are the mirror image of a capacitor, which starts as a wire and ends as a break. Nothing here is examined in AP Physics 2.

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