In the circuit shown in figure power factor of box is `0.5` and power factor of circuit is `sqrt3/2` .Current leading the voltage. Find the effective resistance of the box.

Answer

A

Explanation

`cos phi_1=0.5`
`:. cosphi_1=60^@`
`cosphi_2=sqrt3/2`
`:. phi_2=30^@`
Let `R` be the effective resistance of the box.Then
`tan phi_1=X_C/r` or `sqrt3=X_C/R`....(i)
`tanphi_2=X_C/(R+10)` or `1/sqrt3=X_C/(R+10)`…(i)
From these two equation we get `R=5 Omega`.