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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 100 Ω,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms of voltage is 141 V.
(c) what will happen if the ac source is replaced by a dc source
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Solution
(a) We have,
Φ = π/4
tan Φ = 1
`tanphi = "Reactance"/"Resistance"`
Reactance = Resistance
Y = 100 Ω
As, ϕ > 0°, means voltage ahead of current Hence element Y is an Inductor.
(b)
`"R.m.s value of current" = "R.m.s value of voltage"/"Impedance"`
`"i"_"Rms" = 141/sqrt((100)^2+ (100)^2)`
`"i"_"Rms" = 141/(100sqrt2) = 141/(100 xx 1.41)`
iRms = 1 A
(c) If the Ac is Replace by DC, then the Inductor will behave as a short circuit, and the circuit will be purely Resistive.
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