Question

A resistro R and an element X are connected in series to a.c. source of voltage. The voltage is found to lead the current in phase by `pi//4`. If X is replaced by another element Y, the voltage lags behind the current by `pi//4`. Identify elements X and Y. when both X and Y are connected in series with R, to the same, will the power dissipated in the circuit be maximum of minimum ? Justify you answer.

Answer 1

As the voltage leads the current, X must be inductor (L).
In RL circuit, `"cos" (pi)/(4) = (R )/(Z) = (1)/(sqrt2)`
`X_(L) = sqrt(Z^(2) - R^(2)) = sqrt(2R^(2) - R^(2)) = R`
Again, as voltage lags behind the current, Y must be a capacitor.
`"cos" (pi)/(4) = (R )/(Z) = (1)/(sqrt2)`
`X_(L) = sqrt(Z^(2) - R^(2)) = sqrt(2R^(2) - R^(2)) = R`
Clearly, `X_(L) = X_(C ) = R`
The circuit is purely resistive Impeance is minimum and current is maximum. Hence power dissipated in the circuit is maximum.