A series RLC circuit consists of a 100 W resistor, a 0.15 H inductor, and a 30 µF capacitor. It is attached to a 120 V/60 Hz power line (the voltage 120V is the root mean square value). What are



a. The emf εrms


b. The phase angle ϕ


c. The average power loss

Answers

Answer 1
B……………………………………………..
Answer 2

(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.

Capacitive and inductive reactance of the RLC circuit

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

Impedance of the circuit

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]

Rms current of the circuit

[tex]I_{rms} Z = V_{rms}\\\\I_{rms} = \frac{V_{rms}}{Z} \\\\I_{rms}= \frac{120}{104.96} \\\\I_{rms}= 1.14 \ A[/tex]

Phase angle

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]

Average power loss in the circuit

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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