In the circuit shown in the figure the component in the upper branch is an ideal fuse. It has zero resistance as long as the current through it remains less than 3.0 A. If the current reaches 3.0 A, it “blows” and thereafter it has infinite resistance. Switch S is closed at time . We have to find the time when the fuse blows.

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Until the fuse blows the flow of current in the circuit is determined by the equation

As and L have constant values, variation of current as a function of time will be given by

,

where we have used the boundary condition that at , .

We note that the current through the circuit that also flows through the fuse will increase to at