Max power delivered to variable resistor

In summary, to determine the maximum power that can be delivered to the variable resistor R in the circuit shown in Fig 4.139, you need to find the Thevenin equivalent resistance and voltage. To find R_{th}, you must short the voltage source and find the equivalent resistance between the red nodes. To find V_{th}, use nodal analysis to find the open circuit potential difference across the red nodes with the voltage source added back in. Once you have both values, you can use the formula for the maximum power theorem to calculate the maximum power that can be delivered to R.
  • #1
enian
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0

Homework Statement


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Determine the maximum power that can be delievered to the varaible resistor R in the circuit of Fig 4.139.


Homework Equations





The Attempt at a Solution



I am not sure how to handle this because the resistor is in that diamond structure. I need to find V thev and R thev Any advice or a hint to get started?
 
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  • #3
To find [tex]R_{th}[/tex], short the voltage source. That means drawing a vertical line connecting the blue nodes in your 2nd diagram. Then you must find the equivalent resistance between the red nodes. You have to redraw the circuit in order to solve it easily.

Next to find [tex]V_{th}[/tex], from the original diagram find the open circuit potential difference across the red nodes with the voltage source added back in. That would be the thevenin voltage. You can use nodal analysis to solve this. I got 30V for this. Once you got both, you can use the formulae for the maximum power theorem to get the answer.
 

1. What is the definition of "max power delivered to variable resistor"?

The maximum power delivered to a variable resistor refers to the maximum amount of electrical power that can be transferred to the resistor without causing damage or exceeding its capabilities.

2. How is the maximum power delivered to a variable resistor calculated?

The maximum power delivered to a variable resistor is calculated by taking the square of the current flowing through the resistor and multiplying it by the resistance value of the resistor. This can be represented by the formula P = I^2 * R.

3. What factors affect the maximum power delivered to a variable resistor?

The maximum power delivered to a variable resistor can be affected by various factors such as the resistance value of the resistor, the current flowing through it, and the heat dissipation capabilities of the resistor. Additionally, the surrounding temperature and the material of the resistor can also play a role in determining the maximum power.

4. Why is it important to consider the maximum power delivered to a variable resistor?

It is important to consider the maximum power delivered to a variable resistor because exceeding this limit can lead to overheating and potentially damaging the resistor. This can affect the overall performance and lifespan of the resistor, as well as impact the circuit it is a part of.

5. How can the maximum power delivered to a variable resistor be increased?

The maximum power delivered to a variable resistor can be increased by either increasing the resistance value of the resistor or by reducing the current flowing through it. Additionally, using a resistor with a higher power rating and ensuring proper heat dissipation can also help increase the maximum power.

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