50. The hint is in the problem.
51. What is the EMF across the toroid? If you can give two different answers to this question, you are home free.
52. The purpose of this and the next problem is to
provide the tools needed to get the boundary conditions that must be
used to solve circuits that contain inductors and have time-dependent
currents.
(a). Can the current through an inductor change abruptly? (If it
did, what would the potential drop across the inductor be?)
(b). After the switch has been closed a long time, all currents
become constant. In that case, what is the potential drop across the
inductor?
53. The current cannot change abruptly but its derivative can. [Why and why not?]
54. The problem itself has a broad hint.
I(t) = (V/R)(1 - e- R t / L ),
and the power going into making the magnetic field in the inductor is just
P(t) = dE(t)/dt = I(t)V(t)
where V(t) is the voltage drop across the inductor. You could also find a formula for the energy stored in an inductor, similar to the one for the capacitor. The power formula is of course valid for the battery and for capacitors as well, and it gives the power dissipated in a resistor.
| Last revised 1998/04/16 |