Question

A 70 Ω resistor, an 7.0 μF capacitor, and a 34 mH inductor are connected in series in an ac circuit. -Calculate the impedance for a source frequency of 300 Hz. -Calculate the impedance for a source frequency of 30.0 kHz.

Answer 1

Part A

when f = 300 Hz

Impedance is given by:

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

R = 70 ohm

XL = w*L = 2*pi*f*L = 2*pi*300*34*10^-3 = 64.1 ohm

Xc = 1/(2*pi*f*C) = 1/(2*pi*300*7*10^-6) = 75.8 ohm

Z = sqrt (70^2 + (64.1 - 75.8)^2) = 70.97 ohm = 71 Ohm

Part B.

when f = 30 kHz = 30000 Hz

Impedance is given by:

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

R = 70 ohm

XL = w*L = 2*pi*f*L = 2*pi*30000*34*10^-3 = 6408.8 ohm

Xc = 1/(2*pi*f*C) = 1/(2*pi*30000*7*10^-6) = 0.758 ohm

Z = sqrt (70^2 + (6408.8 - 0.758)^2) = 6408.4 ohm

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