Question

 

An RLC series circuit has a 180 ? resistor and a 25.0 mH inductor. At 7600 Hz, the phase angle is 45.0°.

(a)

What is the impedance (in ohms)? ?

(b)

Find the minimum possible capacitance (in nanofarads) of the circuit.

  nf

(c)

If

V_rms = V

is applied, what is the average power (in watts) supplied?

  W

he lowest frequency in the FM radio band is 87.5 MHz.

(a)

What inductance (in µH) is needed to produce this resonant frequency if it is connected to a 2.45 pF capacitor?

µH

(b)

The capacitor is variable, to allow the resonant frequency to be adjusted to as high as 108 MHz. What must the capacitance be (in pF) at this frequency?

pF

Answer 1

Inductive reactance

X_L=2pifL =2pi*7600*(25*10^-3)

X_L=1193.805 ohms

Power factor

Cos(45)=R/Z

=>Z=180/Cos(45)

Z=254.56 ohms

b)

Since Impedance is

Z=sqrt[R²+(X_L-X_C)²]

254.56 =sqrt[180² + (1193.805-X_C)²]

X_C=1013.805 ohms

SInce X_C =1/2pifC

=>C=1/2pi*7600*1013.805

C=20.66 nF

c)

Vrms value is not given

Current

I=V/Z

Average Power

P_av=VICos(o) =VICos45

substitute value and get the P_av Value

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a)

Resonant frequency

f=1/2pisqrt(LC)

=>L=1/4pi²f²C =1/4pi²*(87.5*10⁶)²*(2.45*10^-12)

L=1.35 uH

b)

Capacitance is

C=1/4pi²f²L =1/4pi²*(108*10⁶)²*(1.35*10^-6)

C=1.6086 pF