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Question
An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi /4` . If element X is a pure resistor of 100Ω ,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms value of voltage is 141V.
(c) what will happen if the ac source is replaced by a dc source ?
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Solution
(a) Since current is leading voltage by `pi/4`, current leak in capacitive curcuit as X is pure resistor therefore Y capacitor.
(b) `phi = tan ^(-1) ((X_c - X_L)/R) X_L = 0`
`pi/4 = tan^(-1)((X_c)/R)`
`(X_c)/R= tan pi/4`
`(X_c)/R= 1` Xc = R
Xc = 100 Ω
`t = sqrt((100)^2 + (100)^2)`
`t = 100 sqrt(2) Omega = 100 xx 1.41 = 141 Omega `
`i_(RMS) = (e_(RMS))/z = 141/141 = 1A`
iRMS = 1A
(c) If we replace ac source by dc ω = 0
`X_c = 1/(omega _c)`
`X_c = 1/0 = ∞ Omega`
`i = e/z = 141/ ∞ `
i = 0
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