How to find the inductance

Question

Hi, I cannot seem to find the exact equation to answer a question regarding a R-C? series circuit (resistor and coil?)

R = 5Ω

I = 20A

Vs = 200v, 50Hz

I need to calculate Z, the value of the inductor (Xl), and the phase angle.

I believe that

Z = √Xl² + R²

Xl = 2πfl

My question is, how would i solve this as i am very confused how to rearrange

Answer 1

Let V_s/I = Z = √( w²L² + R²) then 200/20 = 10 = √( w²L² + R²) = √(4π²L² + 25) now 100 = 4π²L² +25 and

4π²L² = 75 solving for L gives L =1.378h. The phase angle is cosφ = R/Z = 5/10 =1/2 and the phase angle is 60º.