In an inductor, the flux linkage Φ is related to current I by which relation?

In an inductor, the flux linkage Φ is related to current I by which relation?

• A. Φ = L I
• B. Φ = I / L
• C. Φ = L / I
• D. Φ = I L^2

Answer: (A)

In an inductor, the flux linkage is the total magnetic flux linked by all the turns of the coil, and inductance is defined as the ratio of this flux linkage to the current. That gives the linear relation Φ = L I: the flux linkage grows directly with current and the constant of proportionality is the inductance L. This ties directly to the fundamental expression for the induced emf, E = - dΦ/dt, which becomes E = - L dI/dt for an ideal inductor. The other forms don’t fit the way inductance is defined or the units involved, so they don’t represent how flux linkage relates to current.

In an inductor, the flux linkage is the total magnetic flux linked by all the turns of the coil, and inductance is defined as the ratio of this flux linkage to the current. That gives the linear relation Φ = L I: the flux linkage grows directly with current and the constant of proportionality is the inductance L. This ties directly to the fundamental expression for the induced emf, E = - dΦ/dt, which becomes E = - L dI/dt for an ideal inductor. The other forms don’t fit the way inductance is defined or the units involved, so they don’t represent how flux linkage relates to current.