Power dissipated in variable resistor?

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SUMMARY

The discussion focuses on the behavior of power dissipation in a variable resistor, particularly how it increases and then decreases based on the load resistance. It establishes that the maximum power transfer occurs at a specific loading resistance, which is related to the internal resistance of the source. The internal resistance is generally considered constant for theoretical calculations, although it may vary slightly in practical applications. Key equations discussed include Py = VI and V = emf - rI, emphasizing the need to eliminate current from these equations to derive a relationship between power and load resistance.

PREREQUISITES
  • Understanding of Ohm's Law and power equations (Py = VI)
  • Familiarity with concepts of electromotive force (emf) and internal resistance
  • Knowledge of maximum power transfer theorem
  • Basic skills in algebra for manipulating equations
NEXT STEPS
  • Learn about the maximum power transfer theorem in electrical circuits
  • Study the effects of internal resistance on circuit performance
  • Explore impedance matching techniques in electrical engineering
  • Investigate the relationship between load resistance and power dissipation in variable resistors
USEFUL FOR

Electrical engineers, physics students, and anyone interested in circuit analysis and power management in electrical systems.

CAH
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See photo!

Why does the power dissipated increase and then decrease (see graph)? Is it something to do with emf?
Also can internal resistance change as the variable resistor increases/decreases or is it always constant?

- this isn't one of the questions they ask I'm just wondering
 

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CAH said:
See photo!

Why does the power dissipated increase and then decrease (see graph)? Is it something to do with emf?
Also can internal resistance change as the variable resistor increases/decreases or is it always constant?

- this isn't one of the questions they ask I'm just wondering

You can derive the power on the variable resistor in terms its resistance. Keep the emf and internal resistance constant.
It is a very important result that the power is maximum at a certain loading resistance - how is it related to the internal resistance of the source?
Have you heard about impedance matching?
 
Internal resistance can be assumed as being fixed for this exercise, though in practice it can be expected to change slightly.

Can you derive an expression for the power in Y, perhaps assume a particular value for r. Then sketch your graph, power versus value of Y.
 
I don't understand this still,

Py= VI
V= emf - rI
Py= (emf - Ir)I ...=0
 
What is the current in the circuit in therms of the emf and the resistors?
 
CAH said:
See photo!

Why does the power dissipated increase and then decrease (see graph)? Is it something to do with emf?
Also can internal resistance change as the variable resistor increases/decreases or is it always constant?

- this isn't one of the questions they ask I'm just wondering
to answer your question, the internal resisitance won't change with respect to the variable resistor
 
CAH said:
I don't understand this still,

Py= VI
V= emf - rI
Py= (emf - Ir)I ...=0
this is a good start. Your problem is you need to get rid I.

In your second equation, try to get rid of I using Y and r
 
CAH said:
See photo!

Why does the power dissipated increase and then decrease (see graph)? Is it something to do with emf?
Also can internal resistance change as the variable resistor increases/decreases or is it always constant?

-
 
Last edited:
Eliminate current from your equations and see what function you get relating the power with the load Y..Also see whether this power is total power or power consumed by load Y..
 
  • #10
Why does the power dissipated increase and then decrease (see graph)?

Power = voltage * current.

Consider two cases...

1) The variable resistor is set to a very high value (eg open circuit) => The current is very low or zero => Power is very low.
2) The variable resistor is set to a very low value (eg short circuit) => Voltage is very low or zero => Power is very low.

So at both ends of the range the power is very low. So no surprise it's higher in the middle.
 

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