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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 = V2/R, P = I2 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 = V2/P, R = P/I2 (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 = I2 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 = I2 x R = 22x6 = 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= V2/R
In the same way, we can find the power on the resistor using the formula: P = V2/R = 122 / 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 = V2/P = 62 / 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 = V2/P = 62 / 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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