In a series `LCR` circuit

Options

A. the voltage `V_(L)` across the inductance leads the current in the circuit by a phase angle of `pi//2`
B. the voltage `V_(C )` across the capacitance lags behind the current by a phase angle of `pi//2`
C. the voltage `V_(R )` across the resistance is in phase with the current
D. the voltage across sereis combination of `L`, `C` and `R` is `V = V_(L) + V_(C ) + V_(R )`

Answer

A,B,C

Explanation

In series `LCR` circuit current remains same.
Let `I = I_(0) sin omega t V_(R ) sin omega t`
`V_(L) = I_(0) X_(L) sin (omega t + (pi)/(2))` , `V_(C ) = l_(0) X_(C ) sin (omega t - (pi)/(2))`
`:. V_(L)` leads the current by a phase angle of `(pi)/(2)` radian.
`V_(C )` lags behind the current by phase angle of `(pi)/(2)` radian.
`V_(R )` is in phase with `I`.
But voltage across series combination of `LCR` is `V`
`sqrt(V_(R )^(2) + (V_(L) - V_(c ))^(2))`