A 75 ohm resistor, a 95 mH inductor and a 55 uF capacitor are connected in serie

Question

A 75 ohm resistor, a 95 mH inductor and a 55 uF capacitor are connected in series with an ac source with amplitude of 50 V.

a) What is the natural angular frequency?

If the source frequency is 50 Hz:

b)What is the driving angular frequency?

c)What is the capacitive reactance?

d)What is the inductive reactance?

e)What is the impedance?

f)What is the phase angle? And does the current lead or lag the voltage?

g)What is the rms voltage?

h) What is the current ampitude for the circuit?

i)What is the rms current?

Explanation / Answer

a)

natural angular frequency

W=1/sqrt[LC] =1/sqrt[0.095*55*10-6]

W=437.5 rad/s

b)

driving angular frequency

W=2pif =2pi*50

W=314.16 rad/s

c)

Capacitive reactance

XC=1/WC =1/314.16*(55*10-6)

XC=57.87 ohms

d)

Inductive reactance

XL=WL =314.16*(95*10-3)

XL=29.85 ohms

e)

Impedance

Z=sqrt[R2+(XL-XC)2]=sqrt[752+(57.87-29.85)2]

Z=80.06 ohms

f)

Phase angle

o=tan-1(XL-XC/R) =tan-1(57.87-29.85/75)

o=20.5o

Since phase angle is positive ,so current lags the voltage

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