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

Answer:

Z = 530.89 ohms

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 :

$Z=\sqrt{R^2+(X_L-X_c)^2} \\\\Z=\sqrt{R^2+(2\pi fL-\dfrac{1}{2\pi fC})^2} \\\\Z=\sqrt{(40)^2+(2\pi \times 60\times 3\times 10^{-3}-\dfrac{1}{2\pi \times 60\times 5\times 10^{-6}})^2} \\Z=530.89\ \Omega$

So, the impedance of the circuit is 530.89 ohms.