An LC circuit consists of a 3.14 mH inductor and a 4.83 ?F capacitor. (a) Find i

Question

An LC circuit consists of a 3.14 mH inductor and a 4.83 ?F capacitor. (a) Find its impedance at 62.5 Hz. (b) Find its impedance at 10.7 kHz. (c) Now a 36.8 ? resistor is added in series with the inductor and capacitor. Find the impedance of this RLC circuit at 62.5 Hz and 10.7 kHz. At 62.5 Hz At 10.7 kHa (d) Compare the values of Z in parts (a) and (b) with those found in part (c), in which there was also a resistor. Why are they similar? (Select all that apply.) At low frequency, the inductor dominates O At high frequency, the capacitor dominates. O At high frequency, the inductor dominates. O The resistor makes little contribution to the total impedance. O At low frequency, the capacitor dominates.

Explanation / Answer

A.

Impedance of LC circuit is given by:

Z = (sqrt (XL - Xc)^2)

Z = |XL - Xc|

XL = w*L = 2*pi*f*L

Xc = 1/wC = 1/(2*pi*f*C)

When f = 62.5 Hz

Z = 2*pi*f*L - 1/(2*pi*f*C)

Z = |2*pi*62.5*3.14*10^-3 - 1/(2*pi*62.5*4.83*10^-6)|

Z = 525.988 ohm = 526.0 ohm

Part B

When f = 10.7 kHz = 10700

Z = 2*pi*f*L - 1/(2*pi*f*C)

Z = |2*pi*10700*3.14*10^-3 - 1/(2*pi*10700*4.83*10^-6)|

Z = 208.02 ohm = 208.0 ohm

Part C

In RLC circuit

Z = sqrt (R^2 + (XL - Xc)^2)

when f = 62.5 Hz

XL - Xc = 526 ohm

R = 36.8 ohm

Z = sqrt (36.8^2 + 526^2) = 526.28 ohm

when f = 10700 Hz

XL - Xc = 208 ohm

R = 36.8 ohm

Z = sqrt (36.8^2 + 208^2) = 211.23 ohm

Part D

Correct options are C, D and E

XL = 2*pi*f*L

when frequency will be high, XL will also be high

Xc = 1/(2*pi*f*C)

Since Xc and f are inversely proportional, SO when f low then Xc dominates.

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