# Ohm’s Law and the Electric Power

The Ohm’s Law Triangle relates in one equation the voltage, the current and resistance. (Resistance = resistors value). A more complete expression of **Ohm’s Law** is achieved using the electric power formula.

Using the known formula of power: P = V x I, (Power = voltage x current), and its variants: V = P/I and I = P/V, additional formulas are obtained.

These new equations allow us to obtain the values of power, voltage, current and resistance, with only two of the four variables.

- Solving for P, we get: P = V
^{2}/R, P = I^{2}x R, P = V x I (watts) - Solving for I, we get: I = V/R, I = P/V, I = (P/R)
^{1/2}(amps) - Solving for R, we get: R = V/I, R = V
^{2}/P, R = P/I^{2}(ohms) - Solving for V, we get: V = (P x R)
^{1/2}, V = P/I, V = I x R (volts)

The following diagram shows a complete summary of the formulas, arranged so that it is easier to memorize.

Note: The square root = ( )^{1/2}.

## Examples

**Problem**: Find the power dissipated on the resistor R = 6 ohms connected to a battery of 12 volts.

1- Solving the problem using the formula: P = I^{2 }x R

The electric current flowing through the circuit is: I = 12 volt/6 ohms = 2 amperes. We can obtain the power dissipated on heat on the resistor using the formula: P = I^{2 }x R = 2^{2}x6 = 24 watts

2 – Solving the problem using the formula: P = V x I

We can find the power on the resistor using the formula: P = V x I = 12 x 2 = 24 watts

3 – Solving the problem using the formula: P= V^{2}/R

In the same way, we can find the power on the resistor using the formula: P = V^{2}/R = 12^{2} / 6 = 24 watts. Using this formula, you don’t need to find the current flowing through the circuit.

**Problem: **What is the maximum current that can flow through a 5 watt resistor, if it is connected to a 6 volt battery?

1- Solving the problem using the formula: I = P/V.

The electric current flowing through the resistor is: 5 watts/6 volts = 0.83 Amps.

2- Solving the problem using the formula: I = V/R.

First, we obtain the resistance using the formula: R = V^{2}/P = 6^{2 }/ 5 = 7.2 Ohms. Then we can obtain the current flowing through the resistor: I =V/R = 6 volts / 7.2 Ohms = 0.83 Amps.

3- Solving the problem using the formula: I = (P/R)^{1/2}

First, we obtain the resistance using the formula: R = V^{2}/P = 6^{2 }/ 5 = 7.2 Ohms. Then we can obtain the current flowing through the resistor: I = (P/R)^{1/2} = (5 watts / 7.2 ohms)^{1/2} = 0.83 Amps.

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