A 25. 0 - mH inductor, a 2.0 0 - %u03BC F capacitor, and a certain resistor are

Question

A 25.0-mH inductor, a 2.00-%u03BCF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 %u03A9, what is the value of the resistor?

A) 284 %u03A9                       B) 200 %u03A9                       C) 100 %u03A9                       D) 552 %u03A9                        E) 579 %u03A9

The answer may not be listed in the suggested answers above (A-E) Please help, with detail, on how to solve this problem! Thanks!

Explanation / Answer

let the value of the resistor be R.so,

Xl=wl

Xc=1/WC

so,

Z=(R^2 + (Xl-Xc)^2)^0.5

or 200=(R^2 + ((2pi*1000*25*10^-3)-(1/(2*pi*1000*2*10^-6)))^2)^0.5

or R=200 ohm

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