Question

Find the impedance of a circuit consisting of a 1.5 kΩ resistor, 6.0 μF capacitor, and 50 mH inductor in series, at a frequency of 10 kHz .

Express your answer using two significant figures.

Answer 1

Given

LCR circuit

with L = 50*10^-3 H, C = 6*10^-6 F, R = 1.5*10^3 Ω

and frequency f = 10000 Hz

   angular freuency W = 2pi*f = 2pi*10000 = 62831.8530

we know that the impedance of an LCR circuit is

  

   Z = sqrt(R^2+(XL - XC)^2)

where XL,Xc are inductive and capacitive reactance

   XL = W*L = 62831.8530*50*10^-3 = 3141.59265 ohm

   XC = 1/W*C = 1/(62831.8530*6*10^-6) = 2.652582 ohm

and resistance is R = 1.5*10^3 ohm

now impedance is Z = sqrt((1.5*10^3)^2+(3141.59265-2.652582)^2) ohm

       z = 3478.93 ohms
       Z = 3.47893 k ohms