# Calculate Inductance of Choke for AC Heater

• rammer
In summary, to determine the inductance of a suitable choke for a 25 W, 100 V heater to be run from a 250 V, 50 Hz sinusoidal AC supply, one can rearrange equations and use the voltage divider formula to find the necessary impedance for the heater. From there, the remaining side of a right triangle can be calculated, allowing for the determination of inductance from reactance. All voltages in this calculation are assumed to be RMS.
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.

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.

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.

gneill said:
(Is that Peak or RMS?)
i guess RMS ... otherwise its specified : "with peak voltage of 250V" ... not sure but generally its like this ...

skeptic2 said:
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

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.

## 1. What is the purpose of calculating the inductance of a choke for an AC heater?

The inductance of a choke for an AC heater is calculated to ensure that the circuit has the correct amount of inductance to limit the flow of current and prevent damage to the heater. It also helps to maintain the stability and efficiency of the circuit.

## 2. How is the inductance of a choke for an AC heater calculated?

The inductance of a choke for an AC heater is calculated using the formula L = (N^2 * μ * A)/l, where L is the inductance, N is the number of turns, μ is the permeability of the core material, A is the cross-sectional area of the core, and l is the length of the core.

## 3. What factors affect the inductance of a choke for an AC heater?

The inductance of a choke for an AC heater is affected by the number of turns, the permeability of the core material, the cross-sectional area of the core, and the length of the core. The inductance can also be affected by the frequency and amplitude of the AC current.

## 4. How does the inductance of a choke for an AC heater impact the efficiency of the circuit?

The inductance of a choke for an AC heater helps to maintain the stability and efficiency of the circuit by limiting the flow of current. This prevents damage to the heater and also helps to reduce energy losses in the circuit.

## 5. Are there any safety precautions to consider when calculating the inductance of a choke for an AC heater?

When calculating the inductance of a choke for an AC heater, it is important to ensure that the current and voltage ratings of the choke are appropriate for the circuit. It is also important to follow proper safety procedures and wear appropriate protective gear when working with electricity.

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