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A 25 (mu)F capacitor, a 0.1 H inductor a...

A `25 (mu)F` capacitor, a 0.1 H inductor and a `25 Omega` resistor are connected in series with an ac source of emf `E=310 sin 314 t`. Find
(a) the frequency of the emf
(b) the impedance of the circuit
(c) the current in the circuit.
(d) the phase angle

Text Solution

Verified by Experts

(a) Given `omega = 314 implies 2pi f=314 implies f=50Hz`
(b) Impendance of the circuit is
`Z=sqrt(R^(2)+(X_(C)_X_(L))^(2))=sqrt(25^(2)+96^(2))=99.2 Omega`
(c) We have to find rms current in hte circuit in the current . It is given by
`I_(v)=(E_(v))/(Z)=(310//sqrt(2))/(99.2)=2.21 A`
(d) Let `phi` be the angle by which current leads emf, then
`tan (phi)=(X_(C)-X_(L))/(R ) =96/25 implies phi =75.4^(@)`
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Knowledge Check

  • A circuit containing a 20 Omega resistor and 0.1 mu F capacitor in series is connected to 320 V ac supply of angular frequency 100 " rad " s^(-1) . The impedance of the circuit is

    A
    `10^(5)Omega`
    B
    `10^(4)Omega`
    C
    `10^(6)Omega`
    D
    `10^(10)Omega`