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How to use different formulas of power ( \$\frac{V^2}{R}\$, \$V \cdot I\$, \$I^2 \cdot R\$ ) at different situations.

Likewise, for instance, i have a heater of 1000W which converts 220 V to power(Heat) in some infrared region, if i calculate output power using \$V\cdot I\$, it seems okay, but when i calculate power using \$\frac{V^2}{R}\$, since there is a coil of high resistance, output power seems surprisingly small.

May be it seems a basic question, but it made me confused.

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    \$\begingroup\$ What "coil of high resistance"? \$\endgroup\$ – Dave Tweed Jan 10 '13 at 12:22
  • \$\begingroup\$ Heating element of high resistance which converts electricity to heat. \$\endgroup\$ – Nishu Jan 10 '13 at 12:25
  • \$\begingroup\$ @Nishu if the heater is a resistive coil type, the resistance would change as the coil heats up. This is similar to what happens with incandescent bulbs. How are you measuring the resistance? \$\endgroup\$ – Anindo Ghosh Jan 10 '13 at 12:33
  • \$\begingroup\$ @AnindoGhosh :I am not measuring resistance, its just a doubt arise while i was thinking, heating element is the same in most of the heating devices, i just referred that as coil, and about change in resistance, will you tell that in detail please. \$\endgroup\$ – Nishu Jan 10 '13 at 12:39
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There's little need to calculate the power of your heater, since you have already said it's a 1000W heater.

However, to address your confusion, your choice of which to use will depend on what values you know. They will all give the same result, and they are related by Ohm's law. Here's how:

You know Ohm's law, voltage equals the product of current and resistance:

\$ E = I R \$

And you know that power is the product of voltage and current:

\$ P = E I \$

Let's say you have a resistor, and you know the voltage across it, and you want to know the power dissipated in that resistor. \$ P = E I \$, but you don't directly know \$I\$, but you can calculate it with Ohm's law:

\$ I = \frac{E}{R}\$

substituting:

\$ P = E(\frac{E}{R}) \$

which simplifies to:

\$ P = \frac{E^2}{R} \$

If you have a 1000W heater which runs at 220V, I can calculate the resistance your heater must have:

\$ 1000W = \frac{(220V)^2}{R} \$

\$ R = \frac{(220V)^2}{1000W} \$

\$ R = 48.4\Omega \$

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  • \$\begingroup\$ 1000 W was its input power specifications, it's not necessary, that output power will also 1000 W, also , V across the heating element is also not necessarily 220 V. 220 V is supplying voltage. \$\endgroup\$ – Nishu Jan 10 '13 at 12:41
  • \$\begingroup\$ @Nishu: it's unlikely the heater would change the voltage. It's true that some of the 1000 W of input may go to running a fan, a lamp, or a motor, but the power consumed by these components is negligible compared to the heating element, and I didn't think the extra complexity was necessary. \$\endgroup\$ – Phil Frost Jan 10 '13 at 12:45
  • \$\begingroup\$ can u tell me order of resistance of heating elements of real life heaters( which we use in cold or for household purposes ) \$\endgroup\$ – Nishu Jan 10 '13 at 12:49
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    \$\begingroup\$ @Nishu: for 220V heaters, \$50\Omega\$ would be a typical value. \$1kW\$ is a good amount of heat, but not so much that it blows a household circuit breaker. The resistance of the heating element does change with temperature (resistance goes up as it gets hotter), so this calculated resistance is the resistance at operating temperature. When off, they usually look like wires. \$\endgroup\$ – Phil Frost Jan 10 '13 at 12:52
  • \$\begingroup\$ oohhh, i read everywhere that they have high resistances, and it made me really confused. It means, resistance of heating element is relatively higher, not in kohms ?? am i right ?? \$\endgroup\$ – Nishu Jan 10 '13 at 12:56
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Given Ohm's law V = I × R, and the definition of power P = I × V, you can derive a couple of other equations:

P = I2 × R and P = V2 / R

You can solve each of the latter two for R:

R = P / I2 and R = V2 / P

Since these equations are all derived from the same place, if you know any two numbers, you can calculate the other two. In this case, you know the voltage and the power. Therefore, the current is:

I = P / V = 4.545 A

And the resistance is:

R = V2 / P = 48.4 Ω

No matter which equation you use to calculate power based on these numbers, you'll get 1000W.

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