Question

An RLC circuit shown above with a peak voltage of 240 V, f = 60 Hz, R = 100 Kilo Ohms, L = 0.5 mH, C = 200 micro Farad.

A) What is the impendance of the circuit?

B) What is the value of the current read by the ammeter?

C) What is the (linear) resonant frequency of the circuit?

Answer 1

A)

impedance = sqrt(R^2 + (WL - 1/WC)^2)

Z = sqrt(10^10 + (2*3.1415*60*0.5*10^-3 -1/(2*3.1415*60*200*10^-6))^2)

Z = 10^5 Ohms

B)

i = V / Z = 240 / 10^5 = 2.4 mA

C)

WL = 1/WC

f = sqrt(1 / (4*3.1415^2*0.5*10^-3*200*10^-6))

f = 503.3 Hz

Answer 2

A)

impedance = sqrt(R^2 + (WL - 1/WC)^2)

Z = sqrt(10^10 + (2*3.1415*60*0.5*10^-3 -1/(2*3.1415*60*200*10^-6))^2)

Z = 10^5 Ohms

B)

i = V / Z = 240 / 10^5 = 2.4 mA

Answer 3

Impedence of RLC circuit is given by Z^2 = R^2 + (XL-Xc)^2
Where XL = WL = 2pifL = 2*3.14* 60 * 0.0005 = 0.1884 ohms
Xc= 1/wC = 1/2pifC = 1/(2*3.14* 60 * 0.2*10^-3) = 13.2 ohms

so Z^2 = 100000^2 + (13.2-0.1884)^2  

A. Z = 100 K ohms

B. Current I = V/Z = 240/100000 = 2.4 mA

C. W^2 = 1/LC

W^2 =1/200*10^-6 * 0.5*10^-3)

W^2 = 10*10^6

W = 3162.67

f = 3162.67/2pi

f = 503.609 Hz