The current, i, in a series RLC circuit when the switch is closed at t = 0 can be determined from the solution of the 2nd-order ODE

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 i 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 = 10 Ω, and C = 80 μF into the expression that were derived in part (a). Make a plot of i versus t for 0 < t < 1 s. (Underdamped response.)

(c) Use the subs command to substitute L = 3 H, R = 200 Ω, and C = 1200 μF into the expression that were derived in part (a). Make a plot of i versus t for 0 < t < 2s. (Overdamped response.)

(d) Use the subs command to substitute L = 3 H, R = 201 Ω, and C = 300 μF into the expression that were derived in part (a). Make a plot of i versus t for 0 < t < 2 s. (Critically damped response.)

Transcribed Image Text:

di + R dt C