Chapter 11, Problem 30P

$$ 30. The current, i, in a series RLC circuit when the switch is closed a t, = 0 can be determined from the solution of the 2nd, order ordinary differential equation (ODE):

$L\frac{d^{2}i}{d{t}^2}+R\frac{di}{dt}+\frac{1}{C}i=0$ where R, L, and C are the resistance of the resistor, the inductance of the inductor, and the capacitance of the capacitor, respectively.

(a) Solve the equation for t in terms of L, R, C, and t, assuming that at t = 0, i = 0, and di/dt,= 8.

(b) Use the subs command to substitute L = 3 H. R = 10O, and C = 80 µF into the expression that was derived in part (a). Make a plot of i versus t for $0\le t\le 1$ s. (Underdamped response.)

(c) Use the subs command to substitute L = 3 H, R = 200 O, and C = l200µF into the expression that was derived in part (a). Make a plot of i versus t for $0\le t\le 2$ s. (Overdamped response.)

(d) Use the subs command to substitute L = 3 H, R = 201 O, and C = 300µF into the expression that was derived in pan (a). Make a plot of i versus t for $0\le t\le 2$ S. (Critically damped response.)