A 25ohm resistor, 0.5H inductor, and a 20uF capacitor are connected in series wi

Question

A 25ohm resistor, 0.5H inductor, and a 20uF capacitor are connected in series with a 120-Hz source. If the rms current in the LRC circuit is 4.5A, then determine the following: A) RMS Voltage across the resistor B) RMS Voltage across the resistor C) RMS Voltage across the capacitor D) RMS Voltage in the LRC combination E) Average power delivered to the LRC circuit F) Sketch a phasor diagram for this LRC circuit A 25ohm resistor, 0.5H inductor, and a 20uF capacitor are connected in series with a 120-Hz source. If the rms current in the LRC circuit is 4.5A, then determine the following: A) RMS Voltage across the resistor B) RMS Voltage across the resistor C) RMS Voltage across the capacitor D) RMS Voltage in the LRC combination E) Average power delivered to the LRC circuit F) Sketch a phasor diagram for this LRC circuit A 25ohm resistor, 0.5H inductor, and a 20uF capacitor are connected in series with a 120-Hz source. If the rms current in the LRC circuit is 4.5A, then determine the following: A) RMS Voltage across the resistor B) RMS Voltage across the resistor C) RMS Voltage across the capacitor D) RMS Voltage in the LRC combination E) Average power delivered to the LRC circuit F) Sketch a phasor diagram for this LRC circuit

Explanation / Answer

Given that

The resistor (R) =25ohm

The inductor(L) =0.5H

The capacitor (C) =20uF =20*10-6F

The frequency of the source(f) =120Hz

The current in the circuit is (I) =4.5A

The rms voltage across the resistor is given by ohm's law

Vrms =Irms*R =(4.5A)(25) =112.5V

The rms voltage across the inductor (Vrms) =Irms*XL =(4.5A)(2*3.14*120*0.5) =1695.6V

The rms voltage across the capacitor is (Vrms) =Irms*Xc =(4.5*1/2*3.14*120*20*10-6F) =298.56V

Now the rms voltage across the LRC circuit is given by

Vrms =Irms*Z

Now the impedance is given that Z =Sqrt(25)2+(376.8-132.66)2 =Sqrt(625+59604.33)=245.416ohm

Vrms =(4.5A)(245.416) =1104.374V

The average power delivered to the LRC ciruit is given by

P =Vrms2/R =48785.765W

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