Why formula for internal resistance for charging battery v = e + Ir

[needingtoknow]

Homework Statement

Why is the formula for internal resistance for a charging battery v = e + Ir?

When the battery is supplying I to the circuit I understand why the terminal voltage, V, equals emf - IR (voltage lost by internal resistance), but if a battery is charging, why is the voltage lost by internal resistance being added to the ideal voltage, e? The resistance is still there right, even if it is charging, so shouldn't the sign in front of Ir still be negative?

 

[gneill]

Consider the direction of the current flowing in each case. What's the direction of the resulting voltage drop across the internal resistor in each case?

 

[needingtoknow]

In the first case if we use conventional current, the positive charges will be flowing toward the negative terminal. In the second case the positive charges will be flowing toward the positive terminal. (positive charges spontaneously move towards the terminal of lower electric potential). In the first case the positive charges are moving spontaneously toward the negative terminal (delta electric potential or voltage = - and delta PE = - ), but in the second case, energy is required to move the positive charges toward the positive terminal, resulting in delta electric potential or voltage to be positive and delta PE to be positive. That makes sense because you are storing electric energy into potential energy to be used at a later time which is what charging a battery is. So voltage drop is -ve in the first case and +ve in the second case. I'm still having some trouble seeing how this connects with the change in sign in the formula for terminal voltage?

 

[gneill]

It's really very simple. Draw the two cases and note the directions of the potential drop on the internal resistance.

 

[HalfLostAndSearching]

I would like to clarify that the formula v = e + Ir is used to calculate the terminal voltage of a battery, not its internal resistance. The internal resistance, r, in this formula represents the resistance within the battery itself, which affects the flow of current and can cause a drop in the terminal voltage.

When a battery is supplying current to a circuit, the terminal voltage (v) is equal to the battery's electromotive force (e) minus the voltage lost due to its internal resistance (Ir). This is because the internal resistance causes a drop in voltage as the current passes through it. Therefore, the sign in front of Ir is negative because it is a voltage loss.

On the other hand, when a battery is being charged, the internal resistance still exists and can cause a drop in the terminal voltage. However, in this case, the voltage lost due to internal resistance is added to the ideal voltage (e) of the battery, resulting in a higher terminal voltage. This is because the battery is receiving energy from an external source, which helps to overcome the voltage drop caused by the internal resistance. Therefore, the sign in front of Ir is positive in this case.

In summary, the formula v = e + Ir is used to calculate the terminal voltage of a battery, taking into account the effects of its internal resistance. The sign in front of Ir can be either positive or negative, depending on whether the battery is supplying or receiving energy.