5. Consider the following R-L-C circuit.

R

This circuit consists of a source with voltage V(t) (volts), a resistor with constant resistance R

(ohms), an inductor with constant inductance L (henries) and a capacitor with constant capaci-

tance C (farads). A differential equation governing the current I(t) (amperes) that flows through

this circuit at time t (seconds) is

dl

I

R = + = = V(t).

+R-

dt2

(a) Assuming that we have L = 1, R=3, C = 0.5, and that the source provides a constant

(DC) voltage of 9 so that V(t) = 9, calculate the general solution for the current as a

function of time.

[4 marks]

(b) If we instead assume that the source provides an oscillating (AC) voltage with frequency 2

(hertz) and magnitude 240 such that V(t) = 240 sin(2t), calculate the general solution for

the current in this case.

[3 marks]

(c) Using your answer from part (b), if we now assume that there is zero current and rate of

change of current at time t = 0, so that

I(0) = I'(0) = 0,

calculate the particular solution of this initial value problem.

[3 marks]