a 10 ohm resistor, a 3 mH inductor, and a 6 muF capacitir are connected in seeri

Question

a 10 ohm resistor, a 3 mH inductor, and a 6 muF capacitir are connected in seeries with a 12 v rms ACpower supply. A) what is resonance frequency in Hz of the circuit? B) if the frequency is set to 90% of the resonance frequency, what is the rms current of the circuit? C) does the voltage lead or lag the current, and by how much? Express in degrees a 10 ohm resistor, a 3 mH inductor, and a 6 muF capacitir are connected in seeries with a 12 v rms ACpower supply. A) what is resonance frequency in Hz of the circuit? B) if the frequency is set to 90% of the resonance frequency, what is the rms current of the circuit? C) does the voltage lead or lag the current, and by how much? Express in degrees a 10 ohm resistor, a 3 mH inductor, and a 6 muF capacitir are connected in seeries with a 12 v rms ACpower supply. A) what is resonance frequency in Hz of the circuit? B) if the frequency is set to 90% of the resonance frequency, what is the rms current of the circuit? C) does the voltage lead or lag the current, and by how much? Express in degrees

Explanation / Answer

Ev ( rms or virtual value of voltage) = 12 Volt

Ev = 0.707 E0                                    ( E0 = maximum value of voltage)

E0 = 12/ 0.707 = 16.9 volts

a) resonance frequency, fr = 1/ 2*pie* ( LC)1/2

    = 1/ 2*3.14*( 3*10-3*6*10-6)1/2                                                   ( i'm considering c= 6 uF ( because its unit is not clearly given)

fr = 1.186*103 hz

b) Iv ( virtual or rms value of current ) = 0.707*I0

I0 ( maximum value of current) = E0 / Z

f = ( 90/100) * 1.186*103

f = 1067.4 hz

Z ( impedance of circuit) = ( R2 + ( XL - Xc)2 ) 1/2                           ------------------------1

XL = wL = 2*pie*f*L

     = 2*3.14*1067.4*3*10-3 = 20.10 ohm

Xc = 1/ wc= 1/ 2*pie*f*c

    = 1/ 2*3.14*1067.4*6*10-6

   = 24.86 ohm

Z = 11.07    ohm                        ( by putting values in eq 1)

I0 = E0/ Z = 16.9 / 11.07

I0 = 1.526 A

so Iv = 1.0793 A

c) in ac circuit containing R,L.C in series phase angle is given by:

tan@ = XL - Xc / R

              = 20.14- 24.86/ 10

@ = - 25.260

-ve sign shows that voltage lags behind the current.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.