Calculating Terminal Voltage of Batteries with Opposing Currents

[pb23me]

Homework Statement

determine the terminal voltage in each battery.
Emf₁=18V
r₁=1 ohm
EMF₂=12V
r₂=2 ohm
R=6.6 ohms
also the batterys currents are opposing each other.

Homework Equations

Vab=emf-Ir

The Attempt at a Solution

i used kirchnoffs rule to find the current I , 18-I6.6-12-I2-I=0 and got I= .625 then i thought i would just use Vab=emf-Ir to find the terminal voltage of each battery however I am not getting the correct answer... could someone please explain this to me i have a test tomorrow morning and i really need to figure this out! the answers i got were 17.375 for the 18V batt and 10.75 for the 12V batt

 

[gneill]

Watch out for the current direction and the thus the polarity of the voltage drop it creates on the internal resistors. If current is being forced into a battery's positive terminal it's possible for it to have a higher terminal voltage than its internal EMF.

 

[pb23me]

so on the larger voltage batt would i use equation Vab=Emf-Ir = 18-(.625*1) and on the batt with voltage being forced across it use Vab=Emf+... idk

 

[pb23me]

what are the equations you would use in this situation?

 

[gneill]

so on the larger voltage batt would i use equation Vab=Emf-Ir = 18-(.625*1) and on the batt with voltage being forced across it use Vab=Emf+... idk

Yes. It can be helpful to sketch in your current and the polarities of the voltage drops across the resistors. You did fine writing the KVL loop equation.