Final answer:
To induce a 50-V emf across a 10-H inductor, the current through it must change at a rate such that the induced emf, which is proportional to this rate of change, equals 50 V. According to the formula E = -L(dI/dt), this requires a current rate of change (dI/dt) of -5 A/s.
Step-by-step explanation:
A 50-V emf can be induced across a 10-H inductor by altering the current flowing through it. According to Faraday's law of electromagnetic induction, the induced emf (E) in an inductor is directly proportional to the rate of change of current through the inductor (dI/dt), and is given by the equation E = -L(dI/dt), where L is the inductance.
To induce a 50 V emf, the current change over time must satisfy the equation:
E = -L(dI/dt)
50 V = -10 H(dI/dt)
The negative sign indicates the direction of the induced emf opposes the change in current, following Lenz's Law.
For example, if the current through the 10 H inductor decreases by 20 A over a period of time (dt), the rate of change of current (dI/dt) needed to induce a 50 V emf would be calculated by rearranging the above equation to solve for dI/dt:
dI/dt = -50 V / 10 H = -5 A/s
This indicates the current should decrease at a rate of 5 A/s to induce a 50 V emf across the inductor.