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## Homework Statement

The power supply in the circuit shown has V(t) =

(120V)cos(ωt), where ω = 310 rad/s. Determine the current

ﬂowing through the resistor at time t = 9.7 s, given R = 600 Ω,

C = 18 mF, and I(0) = 0 A. As a reminder, Kirkhoﬀ’s voltage

law for this circuit (Eq. 8-1.3 in the book) reduces to:

dV/dt = R(dI/dt) + I/C

## Homework Equations

## The Attempt at a Solution

I've tried this about ten times and can't seem to get the right answer:

I found dV/dt = -37200 Sin(wt) (i'll call it v' from now on)

Rearranging the equation to make it in standard form:

dI/dt + (1/RC)I = v'/R

P= 1/RC = .0926

Q=v'/R = -62 Sin(wt)

F = ∫p dt

So e^F = e^.0926 t

and e^-F = e^-.0926 t

This equation was given in class for solving this type of DE:

I = (e^-I)∫Q*e^F dt + c1*e^-F

When plug this into mathematica, it gives me an imaginary answer

Any ideas?