27. A resistor R ( ) and an inductor L ( H) are connected as shown. Initially, the switch is connected to point A and there is no current in the circuit. At the switch is moved from A to B, so that the resistor and the inductor are connected to

( V), and current starts flowing in the circuit. The switch remains connected to B until the voltage on the resistor reaches 5 V. At that time

( ) the switch is moved back to A.

The current i in the circuit can be calculated from solving the differential equations:

during the time from and until the time when the switch is moved back to A.

from the time when the switch is moved back to A and on.

The voltage across the resistor, , at any time is given by .

(a) Derive an expression for the current i in terms of R, L, , and t for by solving the first differential equation.

(b) Substitute the values of R, L, and in the solution for i, and determine the time when the voltage across the resistor reaches 5 V.

(c) Derive an expression for the current i in terms of R, L, and t, for by solving the second differential equation.

(d) Make two plots (on the same page), one for versus t for and the other for versus t for .