This method may be more intuitive for some people.

[Jimmy87]

Homework Statement

Question - Calculate the rate of energy transferred to the 1.5V cell during charging if the potential between X and Y is 1.9V

Homework Equations

P = VI

The Attempt at a Solution

I think I understand how to get the answer. If XY has 1.9V then the resistor will get 0.4V. This will give a current of 0.44A (0.4V/0.6Ω). Using P=VI for the cell, I get 0.44A x 1.5V = 0.6W. However, thinking about it more I have a few questions. I was thinking about why I couldn't use other circuit power equations - P = I²R and P = V²/R but then I realized this would give the power delivered to the internal resistor and not the cell. However, if we work backwards and use P = V²/R for the cell to find R then what does this mean? i.e. we know it has a power of 0.6W and a voltage of 1.5V so R = V²/P = 3.75Ω. Is this right or is it not valid to use it in this context?

Thanks for any help offered.

 

[BvU]

P = I²R

is for resistors where V = I$\times$R. In a (ideal) chemical cell the power is used for something, well, chemical and the voltage does not depend on the current. So you have to revert to P = V$\times$I

In your exercise the non-ideal chemical cell is modeled as an ideal cell with an internal series resistance.
To answer your question you could check that with e.g. a 0.1 $\Omega$ you would get a different answer.

 

[Jimmy87]

is for resistors where V = I$\times$R. In a (ideal) chemical cell the power is used for something, well, chemical and the voltage does not depend on the current. So you have to revert to P = V$\times$I

In your exercise the non-ideal chemical cell is modeled as an ideal cell with an internal series resistance.
To answer your question you could check that with e.g. a 0.1 $\Omega$ you would get a different answer.

Thanks. So if I have understood you correctly you're saying that we can't use P = I²R because this equation comes from V = IR where the voltage across something depends on its current whereas for a cell its voltage is fixed regardless of the current through it?

 

[BvU]

Yep.

 

[CWatters]

P=I^2R would be the power dissipated in the resistor rather than put into the battery.

One other way to do it would be to apply conservation of energy...

Power into battery = power supplied by the battery charger - power dissipated in resistor
= (1.9*0.44) - (0.4*0.44)
= 1.5*0.44
= 0.6W