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A series RCL circuit contains only a capacitor (C = 8.46 μF), an inductor (L = 6.01 mH), and a generator (peak voltage = 77.4 V, frequency = 2.45 x 103 Hz). When t = 0 s, the instantaneous value of the voltage is zero, and it rises to a maximum one-quarter of a period later. (a) Find the instantaneous value of the voltage across the capacitor/inductor combination when t = 4.32 x 10^-4 s. (b) What is the instantaneous value of the current when t = 4.32 x 10^-4 s?

2. Homework Equations

v(t) = V*sin(2pi*ft)

z= square root(R^2 + (Xl-Xc)^2)

I=V/Z

3. The Attempt at a Solution

the instantaneous voltage in part a = 27.77 V. (this is correct)

my answer to part b is incorrect but I don't know why:

X of L=2pi(2450)(.00601)=92.5 Ohms

X of X=1/(2pi(2450)c) = 7.678 Ohms

Z=square root(0^2 - (92.5 - 7.678)^2) = 84.822

I0=V0/Z = 77.4/84.822 = 0.91249 A

I=I0sin(2pi*ft + (pi/2))

I=(0.91249)sin(2pi(2450)(4.34x10^-4) + (pi/2)) = 0.841 A