Electrical Power Equation Contradiction

[FredericChopin]

We know that the rate at which electrical work is done (electrical power) is defined as:

P = I²*R

, or:

P = V²/R

The formula P = V²/R implies that if the resistance of an electrical component (R) (for example, a light bulb) is decreased, the power consumption (P) will increase hence the light bulb will grow brighter. But the formula P = I²*R implies that if R is decreased, P is also decreased and the light bulb will get dimmer.

They can't both be right. What is your answer to this apparent anomaly?

Thank you.

 

[phinds]

But the formula P = I²*R implies that if R is decreased, P is also decreased and the light bulb will get dimmer.

No, that would imply that we could decrease the resistance without changing the current which doesn't make sense. "I" will increase as the resistance decreases and since the "I" term is squared while the "R" term is not squared, clearly this equation says that if you decrease the resistance, you increase the power.

 

[Drakkith]

Consider a circuit with a voltage of 100 volts and 10 ohms of resistance. Current through the circuit will be 10 amps and the power will be P = 100 x 10. This equals 1000 watts of power.

Now, if we double the resistance to 20 ohms, what happens?
Well, then it's P = 100 x WAIT!
Do we really have 10 amps still?

If the voltage is 100 volts, and the resistance is now 20 ohms, that means that current is at 5 amps.
So, P = 25 x 20, or 500 watts. Doubling the resistance halved the power!

Or if we drop resistance to 5 ohms, then P = 400 x 5, or 2,000 watts. Halving the resistance doubled the power!

 

[FredericChopin]

Thank you very much phinds and Drakkith (I understand!)

 

[sardar]

I understand the confusion that arises from the apparent contradiction between these two equations. However, it is important to note that both equations are correct and can be applied in different scenarios.

The equation P = V2/R is known as the power dissipation formula and is used to calculate the power consumption of a component in a circuit. In this case, the voltage (V) remains constant while the resistance (R) changes. Therefore, as the resistance decreases, the power consumption increases, resulting in a brighter light bulb.

On the other hand, the equation P = I2*R is known as the power delivery formula and is used to calculate the power delivered by a source to a component in a circuit. In this case, the current (I) remains constant while the resistance (R) changes. Therefore, as the resistance decreases, the power delivered decreases, resulting in a dimmer light bulb.

It is important to understand the context in which each equation is being applied in order to avoid confusion. In the first scenario, we are looking at the power consumed by a component, while in the second scenario we are looking at the power delivered by a source. Both equations are valid and serve different purposes in understanding electrical power.