Question

An ac generator with Em = 223 V and operating at 399 Hz causes oscillations in a series RLC circuit having R = 222 Ω, L = 147 mH, and C = 23.1 μF. Find (a) the capacitive reactance XC, (b) the impedance Z, and (c) the current.

Answer 1

Xc= 17.267 Ω, Z= 415.5 Ω, I= 0.537 A

Step-by-step explanation:

Em = 223 V

f= 300 Hz, R = 222 Ω, L = 147 mH, C = 23.1 μF

a)

Capacitive reactance = Xc=?

Xc=
`(1)/(2\pi fC)`

Xc=1/2pi *399*23.1*10^-6

Xc= 17.267 Ω

b).

Z=
`√( R^2 + (Xl - Xc)^2)`

Xl= 2π * f * L

Xl= 2π * 399 * 147 *
`10^(-3)`

Xl= 368.5 Ω

Z=
`√( R^2 + (Xl - Xc)^2)` =
`√(222^2 + (368.5 - 17.267)^2)`

Z= 415.5 Ω

c).

Current:

I= V / Z= Em / Z

I= 223/415.5

I= 0.537 A