A series RLC circuit has R = 410 ?, L = 1.30 H, C = 3.1 ? F. It is connected to

Question

A series RLC circuit has R = 410 ?, L = 1.30 H, C = 3.1 ?F. It is connected to an AC source with f = 60.0 Hz and ?Vmax = 150 V.

Suppose the frequency is now increased to f = 86 Hz, and we want to keep the impedance unchanged.

?VR = V ?VL = V Follow the example closely. What is the current Imax? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. ?VC = V -Aug-e-AVL ---Avc —W—00HE R L

Explanation / Answer

initially

R = 410 ohm

xL = 2 pi f L = 2 x pi x 60 x 1.30

xL = 490 ohm

Xc = 1 / (2 pi f C) = 855.7 ohm

Z = sqrt[ R^2 + (xL - Xc)^2] = 549 ohm

then

xL = 2 x pi x 86 x 1.30 = 702.5 ohm

xC = 1 / (2 x pi x 86 x 3.1 x 10^-6) = 597 ohm

549^2 = R^2 + (702.5 - 597)^2

R = 539 ohm ....Ans

(B) phi = tan^-1 [ (XL - Xc) / R]

= tan^-1[ (702.5 - 597)/539]

= 11 deg

(C) I = V / Z = 150 / 549 = 0.273 A

VR = I R = 147.3 Volt

VL = I XL = 192 Volt

Vc = I Xc = 163 Volt

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