Henry (H)

Also called H, Volt-second per ampere

The henry is the SI unit of inductance, equal to one volt-second per ampere. An inductor of one henry produces one volt of induced emf when the current through it changes at one ampere per second.

Only one of the four AP tables of information prints this symbol. The AP Physics C: Electricity and Magnetism unit-symbol table lists henry, H, among its fifteen entries. AP Physics 1, AP Physics 2 and AP Physics C: Mechanics list it nowhere, which is not an oversight: AP Physics 2 has circuits but no inductors, so it has nothing to measure in henries.

The definition follows the printed relation for a self-induced emf:

E=−LdIdt  ⟹  1 H=1 V⋅sA\mathcal{E} = -L\frac{dI}{dt} \implies 1\ \text{H} = 1\ \frac{\text{V} \cdot \text{s}}{\text{A}}

Read it as a sensitivity. A one-henry inductor answers a current changing at one ampere per second with one volt of opposition. The size of the current itself never enters, only its rate of change.

Two other ways to write it, both useful as checks.

  • From L=NΦB/IL = N\Phi_B/I, a henry is a weber per ampere, equivalently T⋅m2/A\text{T} \cdot \text{m}^2/\text{A}. No AP table prints the weber, so prefer the second form.
  • A henry divided by an ohm is a second, which is the check behind the printed LR time constant τ=L/Req\tau = L/R_{\text{eq}}. A henry times a farad is a second squared, which is the check behind ω=1/LC\omega = 1/\sqrt{LC}.

Two further printed relations carry the unit: UL=12LI2U_L = \tfrac{1}{2}LI^2 for the stored energy, and Lsol=μcoreN2A/ℓL_{\text{sol}} = \mu_{\text{core}}N^2A/\ell for a solenoid, which shows the henries are fixed by geometry and core material rather than by the current.

The physics behind it belongs to inductance.

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