Final answer:
The rate of change of the current in the inductor is 40 A/s, calculated using Faraday's law of electromagnetic induction and the formula E = -L(di/dt), given an induced emf of 10 V and an inductance of 0.25 H.
Step-by-step explanation:
To determine the rate of change of current in the inductor, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in any closed circuit is equal to the negative of the rate of change of the magnetic flux through the circuit. For an inductor, this induced emf (E) is also described by the formula E = -L(di/dt), where L is the inductance and di/dt is the rate of change of current.
In the given problem, a changing current induces an emf of 10 V across a 0.25-H inductor. Using the given values, we can calculate the rate of change of current by rearranging the formula to di/dt = E/L.
Substituting the known values, we get:
di/dt = 10 V / 0.25 H
di/dt = 40 A/s
So, the rate at which the current is changing is 40 A/s.