Can Adding Resistance to a Load Increase Maximum Power?

[Idea04]

I need some help to understand the maximum power theorom. From what I understand it states that in order to get maximum power from a source you have to match the resistance of the source to the resistance of the load. Now what i don't understand is how could adding resistance to a load generate more power. I thought electric power traveled a path to least resistance. And if the resistance of the source is high, let's say a kilo-ohm or mega-ohm, wouldn't the power from the source dissipate to nothing if it came across a load of such high resistance. Especially if the voltage from the source was low (lets ay under 3 volts).

 

[berkeman]

I need some help to understand the maximum power theorom. From what I understand it states that in order to get maximum power from a source you have to match the resistance of the source to the resistance of the load. Now what i don't understand is how could adding resistance to a load generate more power. I thought electric power traveled a path to least resistance. And if the resistance of the source is high, let's say a kilo-ohm or mega-ohm, wouldn't the power from the source dissipate to nothing if it came across a load of such high resistance. Especially if the voltage from the source was low (lets ay under 3 volts).

Classic problem -- good for you to understand it. *Given* some source Z (complex in the general case, not just resistive), if you load it with higher than that Z, you get a higher load voltage, but a lower load current. Calculate the result, and please show us your work.

And if you load the source with a lower Z, you get a higher load current, but a lower load voltage. Calculate the result, and please show us your work.

Now, use calculus (differentiate the right equation) to show what the best Zload is (again, complex) for maximum power transfer, given some pre-set source impedance. Please show us your work.

 

[oswaler]

I can provide some clarification on the concept of maximum power theorem and how adding resistance to a load can potentially increase maximum power.

Firstly, the maximum power theorem states that for a given source and load, there is an optimal resistance that will result in the maximum transfer of power from the source to the load. This optimal resistance is known as the "matching" resistance and it is determined by the internal resistance of the source and the load resistance.

Now, let's consider a simple circuit with a voltage source, a load, and a resistor in series. The voltage source has its own internal resistance, which we can denote as Rs. The load also has its own resistance, which we can denote as Rl. The resistor in series can be denoted as R.

When the load resistance is equal to the matching resistance, the maximum power will be transferred from the source to the load. This is because the load resistance is perfectly matched to the internal resistance of the source, allowing for maximum power transfer.

However, if the load resistance is higher than the matching resistance, there will be a decrease in power transfer. This is because the load resistance is now higher than the internal resistance of the source, causing a decrease in the overall current flow and therefore a decrease in power transfer.

On the other hand, if the load resistance is lower than the matching resistance, there will also be a decrease in power transfer. This is because the load resistance is now lower than the internal resistance of the source, causing an increase in current flow and therefore a decrease in power transfer.

So, how does adding resistance to a load potentially increase maximum power? It all comes down to the matching resistance. If the load resistance is initially lower than the matching resistance, adding more resistance to the load will increase the overall load resistance and bring it closer to the matching resistance. This can potentially result in an increase in power transfer.

However, it is important to note that this is not always the case. Adding resistance to a load may also decrease power transfer if the load resistance is initially higher than the matching resistance. Additionally, the voltage from the source also plays a crucial role in determining the power transfer. If the voltage is too low, even with a matching resistance, the power transfer will be low.

In conclusion, the maximum power theorem states that in order to achieve maximum power transfer between a source and a load, the load resistance must be matched to the internal resistance of the source. Adding resistance to