Question

Does inductance depend on frequency?

Answer 1

Hint: Inductance is the property by virtue of which a material opposes the change in current through it. It is also the ratio of flux and current. When the current changes, the flux associated also changes and the opposition is to the change in flux. Due to change in flux an emf is induced.

Complete answer:
Inductance is the property of a material by virtue of which it opposes the change in current through it. Its SI unit is Henry (H). It is given by-
$L=\dfrac{\phi }{I}$
Here, $L$ is the inductance
$\phi $ is the flux associated with the material or circuit
$I$ is the current
An inductor is a device which stores energy as a magnetic field. When a time-varying current is passed through it, due to electromagnetic induction, an emf is induced in it. The voltage induced is directly proportional to the rate of change of current through the inductor, therefore
$e\propto -\dfrac{dI}{dt}$
Here, $e$ is the emf induced
$\dfrac{dI}{dt}$ is the rate of change of current
On removing the sign of proportionality,
$e=-L\dfrac{dI}{dt}$
Since, inductance is a property, it is a constant and does not depend on any factor and hence does not depend on the frequency. The inductance depends on the make of a conductor.
Therefore, the inductance does not depend on the frequency.

Note:
The negative sign in the proportionality between voltage and rate of current change indicates that the voltage induced is opposite to the rate of current change. Faraday's law states that the electromagnetic induction always opposes the cause as it follows the law of conservation of energy.