Final answer:
The current induced by a 10 V emf across a 0.25-H inductor is changing at a rate of 40 A/s, calculated using the formula dI/dt = E / L wherein dI/dt represents the rate of current change.
Step-by-step explanation:
Determining Current in an EMF
To determine the current induced by an electromotive force (emf) of 10 V in a 0.25-H inductor, we use Faraday's Law of Electromagnetic Induction, which states that the induced emf (E) in an inductor is directly proportional to the rate of change of current through it (dI/dt), as given by the equation:
E = L * (dI/dt)
Where:
- E is the emf induced across the inductor.
- L is the inductance of the inductor.
- dI/dt is the rate of change of current with respect to time.
To find the rate of current change, we can rearrange this equation:
dI/dt = E / L
Plugging in the values, we get:
dI/dt = 10 V / 0.25 H
The result dI/dt = 40 A/s tells us that the current is changing at a rate of 40 amperes per second.