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

Z = 138.5 Ω

Step-by-step explanation:

In a series RLC circuit the impedance is

Z =
`√(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 - (1)/(376.99 \ 50 \ 10^(-3)) )^2 }`

Z =
`√(6400 + ( 113.1 - 0.053)^2)`

Z = √19179.6

Z = 138.5 Ω