A 54 ohm resistor is connected in series with a 13-uFcapacitor and a 40.0 Hz, 9.00x10^1(rms) source. Find thefollowing: a) impedance of the circuit b)rms current in the circuit c) what is the value of the indicatior that must be insertedin the circuit to reduce the current to one-half that found in partb? A 54 ohm resistor is connected in series with a 13-uFcapacitor and a 40.0 Hz, 9.00x10^1(rms) source. Find thefollowing: a) impedance of the circuit b)rms current in the circuit c) what is the value of the indicatior that must be insertedin the circuit to reduce the current to one-half that found in partb?
Explanation / Answer
we are givenwith R = 54 C = 13.0 F f = 40.0 Hz Vrms = 9.00 V (a) first we find the reactance from XC = 1 / 2 f C = ....... the impedence of the circuit is givenby ZRC = (R2 +XC2) =....... (b) the rms current in the circuit is givenby IRC,rms = Vrms /ZRC = ......... A (c) the addition of the inductor creates a fullRLC circuit when IRLC,rms= IRC,rms / 2 then we get that ZRLC = 2 ZRC =........ ZRLC2 = R2+ (XL - XC)2 XL = ± ...... as XL must be greater than zerowe must choose positive sign