(a) The root mean square value of current in the circuit is 1.14 A.
(b) The phase angle ϕ of the circuit is 17.7⁰.
(c) The average power loss in the circuit is 136.4 W.
The capacitive and inductive reactance of the series RLC circuit is calculated as follows;
Xc = 1/ωC
[tex]X_c = \frac{1}{2\pi f C} = \frac{1}{2\pi (60)(30 \times 10^{-6})} = 88.42 \ ohms[/tex]
Xl = ωL
Xl = 2πfL
Xl = 2π(60)(0.15)
Xl = 56.55 ohms
The impedance of the circuit is calculated as follows;
[tex]Z = \sqrt{R^2 + (X_c - X_l)^2} \\\\Z = \sqrt{100^2 + (88.42 -56.55)^2} \\\\Z = 104.96 \ ohms[/tex]
[tex]I_{rms} Z = V_{rms}\\\\I_{rms} = \frac{V_{rms}}{Z} \\\\I_{rms}= \frac{120}{104.96} \\\\I_{rms}= 1.14 \ A[/tex]
The phase angle of the circuit is calcuated as follows;
[tex]tan \phi = \frac{X_c - X_l}{R} \\\\tan\phi = \frac{88.42 - 56.55}{100} \\\\tan\phi = 0.3187\\\\\phi = tan^{-1}(0.3187) \\\\\phi = 17.7 \ ^0[/tex]
The average power loss in the circuit is calculated as follows;
[tex]P = I_{rms}^2 Z\\\\P = (1.14)^2 (104.96)\\\\P = 136.4 \ W[/tex]
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