An `L-C-R` series circuit with `L = 0.120 H, R = 240 a`, and `C = 7.30muF` carries an rms current of `0.450 A` with a frequency of `400 Hz`.
(a) What are the phase angle and power factor for this circuit?
(b) What is the impedance of the circuit?
(c) What is the rms voltage of the source?
(d) What average power is delivered by the source?
(e) What is the average rate at which electrical energy is converted to thermal energy in the resistor?
(f) What is the average rate at which electrical energy is dissipated ( converted to other forms) in the capacitor?
(g) In the inductor ?

Answer

A, B, C, D

Explanation

`X_L=2pifL=301Omega`
`X_C=1/(2pifC)=55Omega`
`Z=sqrt(R^2+(X_L-X_C)^2)`
`Z=sqrt(R^2+(X_L-X_C)^2)`
`=sqrt((240)^2+(301-55)^2)`
`=343Omega`
(a) `phi=cos^-1(R/Z)`
`=cos^-1(240/343)`
`=0.697`
Since, `X_LgtX+C`, voltage leads the current.
(b) Impedance `=Z=343Omega`
(c) `V_("rms")=I_("rms")Z`
`=0.45xx343`
`=155V`
(d) `P=I_(rms)^2R`
`=(0.45)^2(240)`
`=48.6W`
(e) `P=P_R=48.6W`
`P_C=0`
(g) `P_L=0`.