n the RLC series circuit shown in Fig. 3 if, v(t) = 60 sin(100t + 60o) V, compute thefollowing.(a) Total Impedance Z(b) RMS value of the current i(t).(c) Voltage across the capcitor vo(t)(d) Average power absorbed by each element in the circuit.(e) Apparent power supplied by the source and the power factor.
Question
n the RLC series circuit shown in Fig. 3 if, v(t) = 60 sin(100t + 60o) V, compute thefollowing.(a) Total Impedance Z(b) RMS value of the current i(t).(c) Voltage across the capcitor vo(t)(d) Average power absorbed by each element in the circuit.(e) Apparent power supplied by the source and the power factor.
Solution
To solve the given problem, we will follow the steps below:
(a) Total Impedance Z: The total impedance Z of the RLC series circuit can be calculated using the formula: Z = √(R^2 + (XL - XC)^2) where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
(b) RMS value of the current i(t): The RMS value of the current can be calculated using the formula: Irms = Vrms / Z where Vrms is the RMS value of the voltage and Z is the total impedance.
(c) Voltage across the capacitor vo(t): The voltage across the capacitor can be calculated using the formula: vo(t) = Vrms * (XC / Z) where Vrms is the RMS value of the voltage, XC is the capacitive reactance, and Z is the total impedance.
(d) Average power absorbed by each element in the circuit: The average power absorbed by each element in the circuit can be calculated using the formula: P = Vrms * Irms * cos(θ) where Vrms is the RMS value of the voltage, Irms is the RMS value of the current, and θ is the phase angle between the voltage and current.
(e) Apparent power supplied by the source and the power factor: The apparent power supplied by the source can be calculated using the formula: S = Vrms * Irms where Vrms is the RMS value of the voltage and Irms is the RMS value of the current.
The power factor can be calculated using the formula: PF = P / S where P is the average power absorbed by each element and S is the apparent power supplied by the source.
By following these steps and plugging in the given values, you can calculate the required quantities for the given RLC series circuit.
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