The first circuit is for \$t\$ (time) \$\le 0\$, and the second is for \$t \ge 0\$.

The book I'm reading says that \$i_L(0^+)=i_L(0^-)\$, but \$i_1(0^-) \neq i_1(0^+)\$ because there are no limitations on the current changing instantaneously at \$t_0\$.

What I don't understand is why \$i_L(0^+)=i_L(0^-)\$, but \$i_1(0^-) \neq i_1(0^+)\$? Wouldn't \$i_L(t)\$ change instantaneously as to whether or not the voltage source would be connected? Why is one instantaneously changeable and not the other?

## Best Answer

We are talking about the mathematical models used to model a lumped-element network.

In this context any current can change instantaneously,

unless there is a reason it can't. The reason why \$i_L\$ can't change instantaneously is that that current flows in an inductor.Current flowing in an inductor cannot change instantaneously. Any attempt to force such a current to change instantaneously would generate a voltage spike of infinite amplitude across the inductor (a Dirac's delta pulse, from a mathematical POV).

In practice, trying to change a current in an inductor abruptly will lead to large voltage spikes (not infinite) until some nonlinear phenomenon will arise in the circuit (e.g. arcing) and will quench the spike.