When a circuit element X is connected across on a.c. source of e.m.f. `220 sqrt2` volt, current of `sqrt2` A flows through it in phase with the voltage. When another element Y is connected across the same a.c. source, the same current flows through the circuit, but it leads the voltage by `pi//2` radian. Name the circuit element X and Y.
Find the current that flows in the circuit when series combination of X and Y is connected across the same source.

Explanation

Here, `E_(v) = 220 sqrt2 V, I_(v) = sqrt2 A`
As current is in phase with the voltage, element X must be a resistor
`R = (E_(v))/(I_(v)) = (220 sqrt2)/(sqrt2) = 220 ohm`
Through Y, current leads the voltage by `pi//2`
`:.` Y must be a resistor
`X_(C ) = (E_(v))/(I_(v)) = (220 sqrt2)/(sqrt2) = 220 ohm`
When series combination of R and C is connected,
`Z = sqrt(R^(2) +X_(C )^(2)) = sqrt(220^(2) + 220^(2)) = 220 sqrt2 ohm`
`I_(v) = (E_(v))/(Z) = (220 sqrt2)/(220 sqrt2) = 1 A`