Calculate Inductance of Choke for AC Heater

[rammer]

Homework Statement

A 25 W (P), 100 V heater (V(h)) is to be run from a (V) 250 V 50 Hz (f) sinusoidal AC supply. Calculate the inductance (L) of a suitable choke to be included in the circuit. Assume its resistance to be negligible.

Homework Equations

P = V(h)*I*cos(alfa)
I = V/Z
Z^2 = R^2 + (2*Pi*f*L)^2

L = ? H

The Attempt at a Solution

I am basically stuck. I tried to rearrange equations to get sth, but I always end up with two unknowns, angle alfa and current I.
And I am not even sure whether I placed voltages to equations correctly.

 

[gneill]

If the heater is rated at 25W @ 100V DC, then presumably using an AC supply you'll want to run it at 100V RMS. The given supply is 250V AC @ 50Hz. (Is that Peak or RMS?)

The heater and choke coil will form a voltage divider. You want the voltage across the heater resistance to be 100V RMS.

 

[skeptic2]

1. Can you calculate the resistance of the heater?
2. Can you calculate the total impedance you need for the heater to dissipate 25 W with 250 VAC instead of 100 VDC?
3. If you've done the 2 items above, you have the hypotenuse and one side of a right triangle. Can you find the remaining side?
4. Calculate the inductance from the reactance.

 

[cupid.callin]

(Is that Peak or RMS?)

i guess RMS ... otherwise its specified : "with peak voltage of 250V" ... not sure but generally its like this ...

1. Can you calculate the resistance of the heater?
2. Can you calculate the total impedance you need for the heater to dissipate 25 W with 250 VAC instead of 100 VDC?
3. If you've done the 2 items above, you have the hypotenuse and one side of a right triangle. Can you find the remaining side?
4. Calculate the inductance from the reactance

i agree with rammer

 

[rammer]

Thank you, I finally figured it out when you put it in your words. It just wanted a change of point of view - so simple now :)

All voltages are RMS and my final method was:

From P = V(h)I found out I, then R of heater. Using I and V found impedance from which inductance can be ascertained.