A 54 ohm resistor is connected in series with a 13-uFcapacitor and a 40.0 Hz, 9.

Question

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

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