A sinsoidal voltage of peak value 200 V and frequency 50 Hz is applied to a series L - C - R circuit in which R = `3 Omega, L = 25 mH and C = 800 mu F`. Find
(a) the impendance of the circuit.
(b) phase difference between the voltage and current. Is the current lagging behind the emf?

Explanation

Here,
Resistance, `R = 3 Omega`
Inductance, `L = 25mH = 25 xx 10^(-3) H`
Frequency, f = 50 Hz
Capacitance, `C = 800 mu F = 800 xx 10^(-6)F`
Peak value `e_(0) = 200V`
(a) Impedance `Z=sqrt(R^(2)+(X_(L)xxX_(C))^(2))`
`sqrt(R^(2)+(2pifL-(1)/(2pifC))^(2))`
`sqrt((3)^(2)+(2pixx50xx25xx10^(-3)-(1)/(2pixx50xx800xx10^(-6)))^(2))`
= `4.9 Omega`.
(b) Power factor, `cos phi = ( R)/(Z ) = (3)/(4.9)`
`rArr " " phi = cos^(-1) ((3)/(4.9))`
`rArr " " phi = 52.3^(@)`
`therefore` Phase difference `phi = 52.3^(@)`
Yes, current is lagging behind the emf,