Finding the Inductance of a coil

[discoverer02]

I'm stumped by the following problem.

To determine the inductance of a coil used in a research project, a student first connects the coil to a 12.0V battery and measures a current of 0.630 A. The student the connects the coil to a 24.0-V(rms), 60.0-Hz generator and measures an rms current of 0.570 A. What is the inductance?

When the coil is hooked up to the battery R = V/I = 12V/0.63A = 19 ohms. I'm not seeing how this comes into play in finding the solution to the problem.

Z = impedance.
w = radial frequency
j = imaginary number
L = inductance
V = Voltage
I = Current

w = 2pi(60Hz) = 377 rad/sec

I(rms) = V(rms)/Z
Z = jwL

0.570A = 24.0V/[jL(377rad/sec)] this isn't right because it produce the right answer.

What am I missing? A nudge in the right direction would be greatly appreciated.

The answer in the back of the book is 99.6 mH.

Thanks.

 

[Janus]

Originally posted by discoverer02
I'm stumped by the following problem.

To determine the inductance of a coil used in a research project, a student first connects the coil to a 12.0V battery and measures a current of 0.630 A. The student the connects the coil to a 24.0-V(rms), 60.0-Hz generator and measures an rms current of 0.570 A. What is the inductance?

When the coil is hooked up to the battery R = V/I = 12V/0.63A = 19 ohms. I'm not seeing how this comes into play in finding the solution to the problem.

Z = impedance.
w = radial frequency
j = imaginary number
L = inductance
V = Voltage
I = Current

w = 2pi(60Hz) = 377 rad/sec

I(rms) = V(rms)/Z
Z = jwL

0.570A = 24.0V/[jL(377rad/sec)] this isn't right because it produce the right answer.

What am I missing? A nudge in the right direction would be greatly appreciated.

The answer in the back of the book is 99.6 mH.

Thanks.

The nudge is that the resistance of the coil is important to the problem. Impedance (Z) is the result of both the inductive reactance and the resistance.

Z =jwL is only true for a circuit with zero resistance.

for a series circuit you would have

Z= R+jwL

And you can treat this coil as an inductance in series with a resistance.

 

[discoverer02]

Bingo!

I got it. Magnitude of Ztotal = 42.1 ohms
R = 19 ohms
w = 377 rad/sec

and (magnitude of Ztotal)^2 = R^2 + (jwL)^2

plug in the numbers, do the math and you get .0996 H.

Thank you very much for the help Janus.