An inductance `L`, a cpacitance `C` and a resistance `R` may be connected to an `AC` souorce of angular frequency `omega` in three different combinations of `RC, RL` and `LC` in series. Assume that `omegaL=1/(omegaC)`. The power drawn by the three combinatios are `P_(1), P_(2), P_(3)` respectively. THen

Options

A. `P_(1)=P_(2) lt P_(3)`
B. `P_(1) gt P_(2) gt P_(3)`
C. `P_(1) = P_(2) = P_(3)`
D. `P_(1)=P_(2) gt P_(3)`

Answer

D

Explanation

When L and C are joined in series, there is no power loss.
`:. P_(3)=0`
There is no loss of power across L or C.
When R and L are joined in series,
the impedance `Z_(1)= sqrt(R^(2)+omega^(2)L^(2))`
and when R and C are joined in series, `Z_(2) = sqrt(R^(2)+1/(omega^(2)L^(2)))`
But it is given that `omega L = 1/(omega C) :. Z_(1) = Z_(2)`
`:.` Powers consumed by the combinations RC and RL are equal i.e. `P_(1)=P_(2)` and `P_(3)=0`
`:. P_(1) = P_(2) gt P_(3)`.