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A capacitor of capacitance 100 muF and a...

A capacitor of capacitance `100 muF` and a coil of resistance `50 Omega` and inductance `0.5 H` are connected in series with `a 110 V, 50 Hz AC` source. Find the rms value of the current.

Text Solution

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Here, `I_(v) = ? R = 50 ohm, L = 0.5 H, C = 100 mu F = 100 xx 10^(-6) F = 10^(-4) F,`
`E_(v) = 110 V, v = 50 Hz, X_(L) = omega v L = 2 pi xx 50 xx 0.5 = 157 ohm`
`X_(C ) = 1//2 pi v xx 10^(-4) = (10^(4))/(2 xx 3.14 xx 50) = 31.85 ohm`
`Z = sqrt(R^(2) + (X_(L) - X_(C )^(2))) = sqrt(50^(2) + (157 - 31.85)^(2)) = 134.8 ohm`
`I_(v) = (E_(v))/(Z) = (110)/(134.8) A 0.816 A`
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