How to predict how frequency effects current at a given voltage?

[Mr Technical Difficulty]

I'm currently trying to learn the equations for inductive reactance, which was going well until I hit a brick wall with the following question:

“A reactor allows a current of 15 Amps to flow from a 230 Volt 50 Hertz supply. Determine the current which will flow at the same voltage if the frequency changes to (A) 45 Hz and (B) 55 Hz. Ignore the resistance.”

Having looked up the answers in the book, I know that they are (A) 15.97 Amps and (B) 13.07 Amps. What the book doesn't tell me however is the formulae used to ascertain these answers. I understand the reasoning for a higher frequency causing a lower current, but in four hours have not been able to figure out how to work it out precisely from the given information.

If any one has any insight into what formulae is used to give these answers it'd be much appreciated, as it's driving me crackers x2!

 

[godfreyl]

If it's a pure inductor, then the answer in the book is wrong. It should be 45Hz => 16.67A and 55Hz => 13.64A. Is that the answer you got?

 

[Mr Technical Difficulty]

Thanks for the response.

Having only tackled much easier questions so far*, I'd failed to come up with any answers at all in fact! Sat scratching my head like a befuddled Gorilla for hours on end.

I'm just not seeing how to accurately predict the current from only the frequency and voltage. May I ask what formulae you used to get the answers that you came up with?



* For example "What is the inductance reactance value of a coil on a 50 Hertz supply with an an inductance of 0.03 Henrys?" 6.284 x 50 x 0.03 = 9.426 Ohms - Those questions aren't a problem.