The instantaneous current and instantaneous voltage across a series circuit containing resistance and inductance are given by `I = sqrt(2)sin (100 t-pi//4)A` and `upsilon = 40 sin(100t)` V. Calculate the resistance ?

Explanation

`i=sqrt(2)sin (100t-pi//4)A" " (because i=i_(0)sin(omega t-phi))`
`upsilon = 40 sin (100 t)V " " (because V = V_(0)sin(omega t))`
`i_(0)=sqrt(2), V_(0)=40, omega = 100, phi = pi//4`
`R = (V_(0))/(i_(0))cos phi = (40)/(sqrt(2))cos.(pi)/(4)`
`R=(40)/(sqrt(2))xx(1)/(sqrt(2))`
`R = 20 omega`