Calculate Power Generated in Battery: Internal/External Resistance

[atavistic]

OK if we have a circuit with a battery of emf e and internal resistance r and external resistance R. We are given that the current in the circuit is I. What is the thermal power generated in the battery and the power developed in it by the electrical forces.

OK straightforward "formula" question you say.

I know that thermal energy is produced due to resistances(only?).IN this case it would be r. So thermal power = I^2r.

Now my second doubt(I hope you got the first question);power developed by the electric force.I "think" that inside a battery the electric force(due to chemical action) generates power = Ie. But the answer is P = -I(e-Ir). Also shoudnt the power be +ve as the battery is actually discharging?

 

[pixchips]

When they talk about internal resistance of a battery they are making a simplified model for a complex behavior. Point is that thermal energy (or any energy loss in an electrical system) is usually modeled as a resistance. For example, an antenna has a resistance that models the energy that is lost due to propagation of energy away from the antenna. A motor can have 'resistance' due to energy transmitted by the shaft to the load. They aren't all thermal, but they all represent energy leaving the system. But your battery is easier: some power gets lost in the internal resistance, some of it goes to the external load (resistor) but ALL of it comes from the chemical energy generated in the battery. So the energy made by the 'electric force' has to be the sum of that lost in the internal and external resistances, which is what your equation is saying.

As far as signs go: they are just conventions. If you define a current going into a box as positive, and one coming out as negative, then you have a net negative power in the battery and a net positive in the load. In this convention, positive means dissipation, and negative means generation. So eI is negative because its power coming into the system and IIr is positive because its power leaving the system. The definition is actually arbitrary.

 

[atavistic]

Thank you pixchips