An RC circuit (see Figure 4) contains a resistor (10 Ω) and a capacitor (0.2 F) linked i...

An RC circuit (see Figure 4) contains a resistor (10 Ω) and a capacitor (0.2 F) linked in series with an electromotive force E(t) = 10 sin 2π t

(a) Use a numerical solver to sketch the graph of the charge on the capacitor versus time for each of the initial conditions Q(0) = -1, -0.75, -0.5, ... ,1 on the time interval [0, 15]. What appears to happen to each of the solutions with the passage of time? Explain what might be meant by a steady-state response.

(b) What is the frequency of the emf? What appears to be the frequency of the steady-state response? Hint: Recall that in the function f (t) = sin ωt, ω is called the angular frequency, the period is given by T = 2π/w, and the frequency is the reciprocal of the period. Think of the frequency as the number of cycles per second, a unit known as Hertz (Hz).