Question

An RLC circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) is shown below. Assume a sinusoidal EMF (voltage) as shown. A) Derive the ODE describing the current in this circuit, I(t). Hints: (1) voltage drop over capacitor is Q(t)/C where Q(t) = ? Idt. See notes for other voltage drops. (2) Appliction of the Kirchoff Loop should result in an integral in your ODE. Get rid of it by differentiating each term in the ODE. B) Solve the ODE, by any "hand" method, to obtain an equation for I(t). C) Given R = 11 ?, L = 0.1 H, C = 10^-2 F, E_0 = 110 V, and ? = 377 rads/s, solve for the current I(t). Assume I(0)=0 and I'(0)=0 (I'(0)=0 here implies that the capacitor is initially uncharged). D) Use MATLAB to plot I(t) from t=0 to t=0.075s. Comment on what you see. E(t) = E_0 sin ?t

          An RLC circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) is shown below.
Assume a sinusoidal EMF (voltage) as shown.

A) Derive the ODE describing the current in this circuit, I(t). Hints: (1) voltage drop
over capacitor is Q(t)/C where Q(t) = ? Idt. See notes for other voltage drops. (2)
Appliction of the Kirchoff Loop should result in an integral in your ODE. Get rid
of it by differentiating each term in the ODE.
B) Solve the ODE, by any "hand" method, to obtain an equation for I(t).
C) Given R = 11 ?, L = 0.1 H, C = 10^-2 F, E_0 = 110 V, and ? = 377 rads/s, solve for
the current I(t). Assume I(0)=0 and I'(0)=0 (I'(0)=0 here implies that the capacitor
is initially uncharged).
D) Use MATLAB to plot I(t) from t=0 to t=0.075s. Comment on what you see.

E(t) = E_0 sin ?t

An RLC circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) is shown below.
Assume a sinusoidal EMF (voltage) as shown.

A) Derive the ODE describing the current in this circuit, I(t). Hints: (1) voltage drop
over capacitor is Q(t)/C where Q(t) = ? Idt. See notes for other voltage drops. (2)
Appliction of the Kirchoff Loop should result in an integral in your ODE. Get rid
of it by differentiating each term in the ODE.
B) Solve the ODE, by any "hand" method, to obtain an equation for I(t).
C) Given R = 11 ?, L = 0.1 H, C = 10^-2 F, E0 = 110 V, and ? = 377 rads/s, solve for
the current I(t). Assume I(0)=0 and I'(0)=0 (I'(0)=0 here implies that the capacitor
is initially uncharged).
D) Use MATLAB to plot I(t) from t=0 to t=0.075s. Comment on what you see.

E(t) = E0 sin ?t

Added by James G.

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