An inductor `(L = (1)/(100 pi) H)`, a capacitor `(C = (1)/(500 pi) F)` and a resistance `(3 Omega)` is connected in series with an AC voltage source as shown in the figure. The voltage of the AC source is given as `V = 10 cos(100 pi t)` volt. What will be the potential difference between A and B ?

Options

A. `8 cos(100 pi t - 127^(@))` volt
B. `8 cos(100 pi t- 53^(@))` volt
C. `8 cos(100 pi t - 37^(@))` volt
D. `8 cos(100 pi t + 37^(@))` volt

Answer

C

Explanation

`z = sqrt(3^(2)+(5-1)^(2))=50 Omega`
`i=2 cos (100pi t+53^(@))`
`V_(AB) =8 cos (100 pit+53^(@) - 90^(@))` volt
`V_(AB)=8 cos(100 pit-37^(@))` volt