Question

Camera flashes charge a capacitor to high voltage by switching the current through an inductor on and off rapidly. In what time must the 0.100 A current through a 2.00 mH inductor be switched on or off to induce a 500 V emf?

a) 0.1 ms
b) 1 ms
c) 10 ms
d) 100 ms

Answer 1

Using Faraday's law, we find that switching the 0.100 A current off in a 2.00 mH inductor to induce a 500 V emf takes approximately 0.4 ms. The closest answer in the options given is b) 1 ms.

Step-by-step explanation:

To solve for the time required to induce a 500 V emf in a 2.00 mH inductor with a current change of 0.100 A, we use Faraday's law of electromagnetic induction, which tells us that the induced emf (ε) in an inductor is equal to the negative change in magnetic flux over time (ε = -L(dI/dt)), where L is inductance and dI/dt is the rate of change of current. Plugging in the values provided, we have:

500 V = (2.00 mH)(0.100 A / Δt)

Solving for Δt gives:

Δt = (2.00 x 10-3 H)(0.100 A) / 500 V = 4 x 10-4 s or 0.4 ms

The closest answer to this is b) 1 ms, which indicates that the current through a 2.00 mH inductor must be switched on or off in approximately 1 millisecond to induce a 500 V emf.