(a) The rms current in the circuit is 2.58 A.
(b) The rms voltage of Vab is 38.7 V, Vbc is 158.83 V, Vcd is 222.93 V, Vbd is 64.11 V, and Vad is 75 V.
(c) The average rate at which energy is dissipated in each of the 3 circuit elements is 193.23 W.
Capacitive reactance of the circuit
The capacitive reactance of the circuit is calculated as follows;
[tex]X_c = \frac{1}{\omega C} = \frac{1}{2\pi fC} = \frac{1}{2\pi \times 550 \times 4.7 \times 10^{-6}} \\\\X_c = 61.56 \ ohms[/tex]
Inductive reactance of the circuit
Xl = ωL
Xl = 2πfL
Xl = 2π x 550 x 25 x 10⁻³
Xl = 86.41 ohms
Impedance of the circuit
[tex]Z = \sqrt{R^2 + (X_L - X_C)^2} \\\\Z = \sqrt{15^2 + (86.41 -61.56)^2 } \\\\Z = 29.03 \ ohms[/tex]
rms current in the circuits
[tex]I_{rms} = \frac{V_{rms}}{Z} \\\\I_{rms} = \frac{75}{29.03} \\\\I_{rms} = 2.58 \ A[/tex]
rms voltage in resistor (Vab)
[tex]V_{ab} = I_{rms} R\\\\V_{ab} = 2.58 \times 15\\\\V_{ab} = 38.7 \ V[/tex]
rms voltage in capacitor (Vbc)
[tex]V_{bc} = I_{rms} X_c\\\\V_{bc} = 2.58 \times 61.56\\\\V_{bc} = 158.83 \ V[/tex]
rms voltage in inductor (Vcd)
[tex]V_{cd} = I_{rms} X_l\\\\V_{cd} = 2.58 \times 86.41\\\\V_{cd} = 222.93\ V[/tex]
rms voltage in capacitor and inductor (Vbd)
[tex]V_{bd} = I_{rms} \times (X_l - X_c)\\\\V_{bd} = 2.58 \times (86.41 - 61.56)\\\\V_{bd} = 64.11 \ V[/tex]
rms voltage in resistor, capacitor and inductor (Vad)
[tex]V_{ad} = I_{rms} \times \sqrt{R^2 + (X_l- X_c)^2} \\\\V_{ad} = 2.58 \times Z \\\\V_{ad} = 2.58 \times 29.03\\\\V_{ad} = 75 \ V[/tex]
Average rate of energy dissipation in the 3 circuit element
[tex]P = I_{rms}^2 Z\\\\P = (2.58)^2 \times 29.03\\\\P = 193.23 \ W[/tex]
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