When the rms voltages `V_(L), V_(C )` and `V_(R )` are measured respectively across the inductor `L`, the capacitor `C` and the resistor `R` in a series `LCR` circuit connected to an `AC` source, it is found that the ratio `V_(L) : V_(C ) : V_(R ) = 1 : 2 : 3`. If the rms voltage of the `AC` sources is `100 V`, the `V_(R )` is close to:

Options

A. `50 V`
B. `70 V`
C. `90 V`
D. `100 V`

Answer

3

Explanation

Given, `V_(L) : V_(C ) : V_(R ) = 1 : 2 : 3`
`V = 100 V`
`V_(R ) = ?`
As we know,
`V = sqrt(V_(R )^(2) + (V_(L) - V_(C ))^(2))`
Solving we get, `V_(R ) = 90 V`