How to use different formulas of power ( \$\frac{V^2}{R}\$, \$V \cdot I\$, \$I^2 \cdot R\$ ) in different situations?
For example, 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, the output power seems surprisingly small.
May be it seems a basic question, but it confused me.
Best Answer
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 \$