An RC circuit (see Figure 4) contains a resistor (10 ohms) and a capacitor (0.2 F) linked in series with an electromotive force E(t) = 10 sin 2πt. (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
An RC circuit (see Figure 4) contains a resistor (10 ohms) and
a capacitor (0.2 F) linked in series with an electromotive
force E(t) = 10 sin 2πt.
(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/ω,
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).
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