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A circuit conatining of a capacitor and ...

A circuit conatining of a capacitor and an active resistance R=`110 Omega` connected in series is fed and alternating voltage with amplitude` V_(0) = 110V` . In this case, the amplitude of current is equal to `I_(0) = 0.50A`. Find the phase difference between the current and the voltage fed .

Text Solution

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Consider an RC circuit as shown below

Given, `I_(0) = 0.50 A`
`therefore I_(0) = V_(0)/Z implies 0.5 = 110/Z implies Z = 220 Omega `
` implies Z^(2) = R^(2) + X_(C)^(2) implies (220)^(2) = (110)^(2) + X_(C)^(2)`
`implies X_(C)^(2) = (220)^(2) - (110)^(2) = 330 XX 110`
`implies X_(C) = 110sqrt 3 Omega `
Now we can write
`tanphi = X_(C)/R = (110sqrt 3)/110 = sqrt 3 implies phi = 60^(@)`
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