Why Does External Resistance Equal Internal Resistance for Maximum Power?

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In summary, the maximum power delivered by a battery to an external resistance network occurs when the external resistance equals the internal resistance. This is because the power equation, P=I^2*R, shows that greater external resistance leads to greater power, even if it exceeds the internal resistance. To find the exact condition for maximum power delivery, one can use the equation P=VI and find dP/dR, then equate it to zero.
  • #1
sArGe99
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Homework Statement


My textbook says that the power delivered by the battery to external resistance network will be maximum when the external resistance equals the internal resistance? Why is it so?
p = I^2 * R, so greater the external resistance, greater the power(even if it exceeds internal resistance)

Homework Equations


P = VI ;)


The Attempt at a Solution


Clueless about this one.
 
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  • #2
In the circuit the current is written as
I = E/(R + r) where E is the emf of the battery and r is the internal resistance of the battery.
So P = I^2*R =[ E^2/(R + r)^2]*R
The power delivered by the battery depends on the external resistance. So find
dP/dR and equate it to zero to get the condition for maximum power delivery
 
  • #3
Thanks a lot. :cool:
 

1. Why is external resistance equal to internal resistance for maximum power?

According to Ohm's Law, power is calculated by multiplying the current (I) by the voltage (V). In order to achieve maximum power, the resistance (R) must be at its optimum value. When external resistance is equal to internal resistance, the overall resistance in the circuit is minimized, allowing for maximum current to flow and thus maximizing power output.

2. Can external resistance be greater than internal resistance for maximum power?

No, external resistance cannot be greater than internal resistance for maximum power. This is because a higher external resistance would result in an overall increase in resistance in the circuit, reducing the current flow and therefore decreasing power output.

3. How does changing the external resistance affect power output?

Changing the external resistance in a circuit affects power output by altering the overall resistance in the circuit. When external resistance is increased, the overall resistance also increases, resulting in a decrease in current flow and therefore a decrease in power output. Similarly, decreasing external resistance will decrease overall resistance and increase power output.

4. What is the relationship between internal resistance and maximum power?

The internal resistance of a power source determines the maximum power that can be delivered to an external load. A lower internal resistance allows for a greater current flow and thus a higher power output. Conversely, a higher internal resistance will limit the current flow and decrease power output.

5. How does the type of circuit affect the equality of external and internal resistance for maximum power?

The equality of external and internal resistance for maximum power applies to simple circuits with a single power source. In more complex circuits, such as those with multiple power sources or non-linear elements, the relationship between external and internal resistance for maximum power may not hold true.

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