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An a.c. circuit consists of a series com...

An a.c. circuit consists of a series combination of circuit elements X and Y. The current is ahead of voltage in phase by `pi//4`. If element X is a pure resistor of 100 ohm, name the circuit element Y, and calculate the rms value of current if rms voltage is 141 V.

Text Solution

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As current is ahead of voltage, the circuit element Y must be a capacitor.
As `cos phi = (R )/(Z) = "cos" (pi)/(4) = (1)/(sqrt 2)`
`Z = R sqrt2 = 100 xx 1.414 = 141.4 Omega`
`I_(v) = (E_(v))/(Z) = (141)/(141.4) ~= 1 A`
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