Question

When alternating current flows through a conductor, the flux change:
(A) is higher in the inner part of the conductor
(B) is lower in the inner part of the conductor
(C) is uniform throughout the conductor
(D) Depends upon the resistivity of the conductor

Answer 1

Hint: Alternating current is one in which the direction of current changes in every particular fixed time and this time is called its time period and inverse of the time period called its frequency of an alternating current while direct current always flows in only one particular direction.

Complete step-by-step solution:
Let us suppose the current flowing in an AC circuit is given as:
$i = {i_0}\sin (\omega t + \theta )$ Now, we need to determine the rate of change of flux
As, flux $\phi = Li$
Change of flux is:
$\dfrac{{d\phi }}{{dt}} = L\dfrac{{di}}{{dt}}$
Which can be written as
$\dfrac{{d\phi }}{{dt}} = L{i_0}\dfrac{{d\sin (\omega t + \theta )}}{{dt}}$
$\dfrac{{d\phi }}{{dt}} = L{i_0}\omega \cos (\omega t + \theta )$
Since, $L$ is the inductance of the conductor which remains constant with time
${i_0}$ Is the maximum value of current in alternating circuit so, its value also remain fixed with time
Hence, the rate of change of flux is not dependent upon the inner or outer radius or lengths of the conductor, its remaining constant uniformly throughout the whole conductor.
Hence, the correct option is (C) is uniform throughout the conductor.

Note: Since, alternating current direction changes with time so, the direction of flux changes with the direction of current in every phase but the magnitude of rate of change of flux remains same in every phase and is always independent of length and have a uniform constant value with time.