A resistor of 200 `Omega`, an inductor of 25 mH and a capacitor of 15.0 `mu`F are connected in series to a 220 V, 50 Hz ac source. Calculate the current through the circuit. Also find the phase difference between the voltage across the source and the current.

Explanation

Given : `R=200 Omega, L = 25mH = 25 xx 10^(-3)H, C = 15.0 muF = 15xx10^(-6)F`, V = 220V, v= 50 Hz
Impedence,
`Z= sqrt(R^2 +(X_L - X_C)^2)` and `X_L = omega L = 2pi vL = 2xx3.4 xx 50 xx 25 xx 10^(-3)`
`X_L = 7850xx10^(-3)`
`X_L= 7.850 Omega`
`X_C =(1)/(omega C)=(1)/(2pi vC)=(1)/(2xx3.4xx 50 xx25xx10^(-6))`
`X_C=(1)/(4710xx10^(-6))`
`X_C = 0.0002123xx10^6`
`X_C = 212.3 Omega`
`Z=sqrt((200)^2 + (7.850 - 212.3)^2)`
`=sqrt((200)^2 +(-204.45)^2)`
`=sqrt(40000+41799.80) = sqrt(81.799.8)`
`Z=286.006 Omega`
i) Current in the circuit
`I_("rms")=(V_("rms"))/(Z)=(220)/(286.006)`
`I_("rms")= 0.7692 A`
ii) The phase difference between the current and voltage is given by `tan phi =(X_L -X_C)/(R)= (7.850 -212.3)/(200)`
`tan phi =(204.45)/(200)`
`tan phi =1.0222`
`phi = tan^(-1)(1.0222)`