Choose the correct relation out of the following.

The correct answer is Option (2) → \( 1\,\mathrm{H}=\frac{1\,\mathrm{V}}{1\,\mathrm{A\,s^{-1}}} \)

The self-induced emf is \( \varepsilon=-L\,dI/dt \), so in magnitude the inductance is the emf per unit rate of change of current:

    \( \displaystyle L=\frac{|\varepsilon|}{dI/dt} \)

Hence a coil has an inductance of \( 1\,\mathrm{H} \) when a current changing at \( 1\,\mathrm{A\,s^{-1}} \) induces an emf of \( 1\,\mathrm{V} \) in it.

Option (1) \( 1\,\mathrm{H}=\frac{1\,\mathrm{V}}{1\,\mathrm{A}} \) — Incorrect. Volt per ampere is the ohm, the unit of resistance (\( R=V/I \)). Inductance divides the emf by the rate of change of current.

Option (2) \( 1\,\mathrm{H}=\frac{1\,\mathrm{V}}{1\,\mathrm{A\,s^{-1}}} \) — Correct. Putting the units into \( L=|\varepsilon|/(dI/dt) \) gives volt divided by ampere per second, so \( 1\,\mathrm{H}=1\,\mathrm{V\,s\,A^{-1}} \).

Option (3) \( 1\,\mathrm{H}=\frac{1\,\mathrm{A}}{1\,\mathrm{V}} \) — Incorrect. Ampere per volt is the reciprocal of the ohm. It has the current in the numerator, but inductance has the emf in the numerator.

Option (4) \( 1\,\mathrm{H}=\frac{1\,\mathrm{V}}{1\,\mathrm{A\,s}} \) — Incorrect. The denominator must be a rate of change of current, ampere per second. The product \( \mathrm{A\,s} \) is the coulomb, a unit of charge, so this ratio is volt per coulomb.

NCERT (2026-27):
Self-inductance – “… When the current is varied, the flux linked with the coil also changes and an emf is induced in the coil. … the induced emf is given by

    \( \displaystyle \varepsilon=-L\frac{dI}{dt} \)\( \qquad (6.14) \)”

Inductance – “… The SI unit of inductance is henry and is denoted by H.”