An AC voltage of the form V = (120 V) sin (290 t ) is applied to a series RLC ci

Question

An AC voltage of the form V = (120 V) sin (290t) is applied to a series RLC circuit. IfR = 56 , C =30 µF, and L =0.22 H, find the following. (a) impedance of the circuit
1

(b) rms current in the circuit
2 A

(c) average power delivered to the circuit
3 W


I have been making mistakes on the calculations, so please work itout and respond with a numerical value, thank you verymuch....
(a) impedance of the circuit
1

(b) rms current in the circuit
2 A

(c) average power delivered to the circuit
3 W


I have been making mistakes on the calculations, so please work itout and respond with a numerical value, thank you verymuch....

Explanation / Answer

Given : .          V = (120 V) sin(290t)     it is compared to  V   = Vo   sin(2f t) . We know that : .               Impedance Z = (XL -XC )2 + R2  -------(1) . Here R = 56 ;  XL = 2f L = 290 *0.22 = 63.8 .        XC = 1/ 2fC = 1 / (290 * 30 * 10-6) = 114.94 . Hence    Z =   ( 63.8 -114.94 )2 + 562   = 75.84 . (b)    Irms  =   Vrms / Z .                  = Vo /Z*2                            ( since   Vrms    = Vo / 2   ) .                  = (120 /( 75.84 * 2) ) = 1.1188 A . (c)   Average power delivered is : .             P =  ( Irms  )2 Z  cos   ----------(2) . Here        = tan-1 [ ( XL - XC ) / R ]   . Plug all the values in eqn (2) to get "P" value. . Hope this helps u!

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