An electrical device draws 2 kW power form AC mains [voltage 223 V (rms) `= sqrt(50,000) V`]. The current differs (lags) in phase by `phi (tan = (-3)/(4))` as compared to voltage. Find (i) R, (ii) `X_(C ) - X_(L)`, and (iii) `I_(M)`. Another device has twice the values for R, `X_(C )` and `X_(L)`. How are the answers affected ?

Explanation

`P = 2KW = 2000W, tan phi = (-3)/(4) , I_(m)=I_(0) ? R = ? X_(C)- X(L)=?`
`V_("rms") = V= 223 V`
`Z = (V^2)/(P) = 25 Omega`
`Z = sqrt(R^2 + (X_(L) - X_(C ))^2)`
`625 = R^2 + (X_(L) - X+_(C ))^2`
Again `tan phi = (X_L - X_C)/ (R ) = (3)/(4)`
`X_(L) - X_( C) = (3R)/(4)`
using this `R= 20 Omega, X_(L) - X_( C) = 15 Omega, I = (V)/ (Z) = (223)/(25) = 8.92 A`
`I_(m) = sqrt(2) I = 12.6 A`