Question

A 50mf capacitor, a 0.3H inductor and an 80 ohm resistor is connected in series with a 120v, 60Hz power source
What is the impedance of a circuit? ​

Answer 1

Answer:

Z = 138.5 Ω

Explanation:

In a series RLC circuit the impedance is

          Z = $\sqrt{R^2 + ( X_L - X_C)^2 }$

the capacitive impedance is

         X_C = 1 / wC

the inductive impedance is

         X_L = wL

in this exercise indicate that C = 50 10⁻³ F, L = 0.3 H and the frequency is f=60 Hz

angular velocity and frequency are related

         w = 2π f

         w = 2π 60

         w = 376.99 rad / s

let's calculate

        Z = $\sqrt{80^2 + ( 376.99 \ 0.3 - \frac{1}{376.99 \ 50 \ 10^{-3}} )^2 }$

        Z = $\sqrt{6400 + ( 113.1 - 0.053)^2}$

        Z = √19179.6

        Z = 138.5 Ω