DC versus AC current in a coil

[IronaSona]

Homework Statement

.

Relevant Equations

XL =2p x f x L.

Hello, am kind of new to all the physics stuff , and kind a terrible at maths but am trying my best to be good at it one day .So i was told to answer this question

When a direct current of 2A is passed through a coil, the potential difference across the coil is 20V. When an alternating current of 2A at a frequency of 40Hz is passed through the coil, the potential difference across the coil is 140V.

a) Find the current in the coil if it is connected to a supply of 230V, 50Hz.

but i don't even know where i need to start ? do i need to find the coil inductances first and then do:
2 = a constant (2 x 3.1416 = 6.28)
6.28*hz*henries= ... Ohms

240V/...Ohms= ...Amps?

is that right ?and for (b) i got no idea how to do that

b) What is the phase shift of the current in the coil with respect to the supply voltage?

 

[vela]

Rather than guessing and plugging numbers into formulas, you need to see the big picture and formulate a strategy. So first, what is the significance of what the sentence below is telling you?

When a direct current of 2A is passed through a coil, the potential difference across the coil is 20V.

 

[IronaSona]

Rather than guessing and plugging numbers into formulas, you need to see the big picture and formulate a strategy. So first, what is the significance of what the sentence below is telling you?

voltage across the coil is 20V?

 

[vela]

That's what the sentence literally says, but what does it mean? Why does the DC current produce a voltage drop across the coil?

 

[IronaSona]

That's what the sentence literally says, but what does it mean? Why does the DC current produce a voltage drop across the coil?

because there's a resistance

 

[vela]

OK, good, so the coil isn't simply an inductor but an inductor $L$ and a resistor $R$.

The second sentence says

When an alternating current of 2A at a frequency of 40Hz is passed through the coil, the potential difference across the coil is 140V.

What's the relationship between those two quantities in terms of $R$, $L$, and frequency $f$? Rather than using numbers, just call them $I$ and $V$ for now.