Question

an rlc series circuit has a 40.0 resistor,a 3.00 mH inductor, and a 5.00 capacitor, (a find the circuits impendance at 60.0 Hz

Answer 1

Z = 530.89 ohms

Step-by-step explanation:

Given that,

Resistor, R = 40 ohms

Inductor, L = 3 mH

Capacitor, C = 5 μF

We need to find the impedance of the circuit at frequency of 60 Hz. For a series LCR circuit, its impedance is given by the formula as follows :

`Z=√(R^2+(X_L-X_c)^2) \\\\Z=\sqrt{R^2+(2\pi fL-(1)/(2\pi fC))^2} \\\\Z=\sqrt{(40)^2+(2\pi * 60* 3* 10^(-3)-(1)/(2\pi * 60* 5* 10^(-6)))^2} \\Z=530.89\ \Omega`

So, the impedance of the circuit is 530.89 ohms.