A series RLC circuit consists of a 57.0 ohm resistor, a 2.40 mH inductor, and a

Question

A series RLC circuit consists of a 57.0 ohm resistor, a 2.40 mH inductor, and a 460 nF capacitor. It is connected to a 3.0 kHz oscillator with a peak voltage of 4.80 V. You may want to review ( pages 1042 - 1046). For help with math skills, you may want to review: Conversion from Degrees to Radians Calculating Trigonometric Function Values What is the instantaneous emf epsilon when i = 7? Express your answer with the appropriate units. What is the instantaneous emf E when i = 0 A and is decreasing? Express your answer with the appropriate units.

Explanation / Answer

w = 2*pi*f = 2*3.14*3000 = 18840 rad/s

xL = wL = 18840*2.4e-3 = 45.216 ohms

xC = 1/wC = 1/(18840*460e-9) = 115.4 ohms

phase difference theta = ? = tan^-1(xC-xL)/R = 0.88 rad

part A)

i = I

I*sin(wt - ? ) = I

sin(wt - ? ) = 1

(wt - ? ) = pi/2

wt = 1.57+0.88

t = 0.13 ms

e = E*sin((18840*0.13e-3)-(0.88)) = 4.8 V

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part B)

i = 0

I*sin(wt - ? ) = 0

sin(wt - ? ) = 0

(wt - ? ) = 0

wt = 0.88

t = 0.047

e = E*sin((18840*0.047)-(0.88)) = -4.7 V

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part C)

i = I

I*sin(wt - ? ) = -I

sin(wt - ? ) = -1

(wt - ? ) = 4.712

wt = 4.712+0.88

t = 0.29 ms

e = E*sin((18840*0.29e-3)-(0.88)) = 0.38 V

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