The current in the coil uniformly changes from 0 to 4 A in 0.5 s. What is the inductance of the coil

The current in the coil uniformly changes from 0 to 4 A in 0.5 s. What is the inductance of the coil if an EMF of 2V self-induction occurs in it.

Task data: I1 (initial value of the current strength) = 0 A; I2 (end value) = 4 A; t (duration of current increase) = 0.5 s; εi (EMF of self-induction arising in the used coil) = 2 V.

We express the inductance of the used coil from the formula: εi = | L * (I2 – I1) / Δt |, whence L = εi * Δt / (I2 – I1).

Let’s calculate: L = 2 * 0.5 / (4 – 0) = 0.25 H.

Answer: The inductance of the coil used is 0.25 H.