Finding inductance when resistor and inductor are in series at 230V

[johnboy14]

Homework Statement

a non inductive resistor passes a current of 20A rms, when connected to a 100v rms supply (50HZ). When connect in series with a pure inductor across a 230v supply the combination draws a current of 15A calculate impedance of the circuit, inductance of the inductor

The Attempt at a Solution

R = 100v/20A = 5 ohms

Z = V/I

Z = 230/15 = 15.3

z = square root R^2 + X^2 Find X^2

Z^2 - R^2 = X^2

SRoot 15.3^2 - 5^2 = 14.45 ohms

From what I found how do I find the inductance of the inductor. I only know one way using flux density but there is no data given on this in the question.

 

[johnboy14]

I know that the formula for reactance is Xl = 2(pi) f L
How do I find L that's the just of what I want.

 

[SGT]

I know that the formula for reactance is Xl = 2(pi) f L
How do I find L that's the just of what I want.

You know that $$X_L = 14.45\Omega$$ anf f = 50Hz.

 

[johnboy14]

Do yous get 21.7 for L

 

[SGT]

Do yous get 21.7 for L

I found 0.0458H

 

[johnboy14]

I found 0.0458H

How did you get that

 

[SGT]

How did you get that

$$L=\frac{X_L}{2\pi\,50}=\frac{14.45}{314.16}=0.0458H$$

 

[johnboy14]

I see I made a substitution mistake in my formula I devided by XL thanks for the help