The voltage time (V-t) graph for triangular wave having peak value `V_(0)` is as shown in figure.The rms value of V in time interval from `t = 0` to `T//4` is

Options

A. 5
B. 4
C. 7
D. 3

Answer

D

Explanation

Given, `V_(0) = 283 "volt", omega = 320, R 5Omega, L = 25 mH, C = 1000 mu F`
`x_(L) = omegaL = 320 xx 25 xx 10^(-3) = 8 Omega`
`x_(c) = (1)/(omegaC) = (1)/(320 xx 1000 xx 10^(-6)) = 3.1 Omega`
Total impedance of the circuit :
`Z = sqrt(R^(2) + (X_(L) - X_(C))^(2)) = sqrt(25 + (4.9)^(2)) = 7Omega`
Phase difference between the voltage and current
`tan phi = (X_(L) - X_(C))/(R)`
`tan phi = (4.9)/(5) approx 1 Rightarrow phi = 45^(@)`