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In an alternaitng current circuit, resis...

In an alternaitng current circuit, resistor, inductor and capacitor are connected in series in diagram shown in Fig. Find the value of current and power foctor of the circuit

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Here, `R = 50 Omega, L = 10 H`
`C = 2 mu F = 2 xx 10^(-6) F, E_(v) = 250 V, v = 50 Hz`
`X_(L) = omega L = 2 pi L = 2 xx 3.14 xx 50 xx 10 = 3140 Omega`.
`X_(C ) = (1)/(omega C) = (1)/(2 pi v C)`
`= (1)/(2 xx 3.14 xx 50 xx 2 xx 10^(-6)) = (10^(4))/(6.28)`
`Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2))`
` = sqrt(50^(2) + (3140 - 1.6 xx 10^(3))) = 1540 Omega`
`I_(v) = (E_(v))/(Z) = (250)/(1540.8) = 0.162 A`
Power factor, `cos phi = (R )/(Z) = (50)/(1540.8) = 0.032`
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