How to Solve for Terminal Voltage in a Circuit with an Unknown Battery

[Angie K.]

Homework Statement

The current through the 4.0 kΩ resistor in the figure above is 2.1 mA. The resistor R is 5.4 kΩ. What is the terminal voltage Vba of the "unknown" battery? (Note there are two possible answers: one positive and one negative. Give the negative voltage first.)

Homework Equations

Vab=E-Ir
I=E/(R+r)
Kirchhoff's Laws (junction and loop rule)

The attempt at a solution
I attempted to use the equation I=E/(R+r) (converting kiloohms to ohms) and using 12V for E, 88000.9 Ohms for R and 5400 Ohms for r. Is that right, or am not supposed to use the 5400 Ohms for the little r? I'm not really sure what to do from here. I know the direction of the current matters and I chose to calculate it where the current flows from the positive end of the battery. But going from there, I'm totally lost.

 

[axmls]

Notice that the 4k resistor is in parallel with the 8k resistor. What does that tell you about the voltage across (and therefore the current through) the 8k resistor? If you know both of those currents, then do you know the current through the large loop? And if you know that, can you then write some loop equations to accomplish your goal?

 

[gneill]

Can you explain why you believe that the equation I=E/(R+r) is applicable here? And where does the value 88000.9 Ohms come from?

I suggest that you start by labeling the circuit diagram with known values (pick a direction for the given current --- you'll be doing it again for the other direction in order to cover the two cases). Then start filling in what you can deduce / calculate starting with the known values. I'll start you off: here's your circuit for when the given current is flowing to the left: Can you find the potential drop across the 4k resistor? How about the current through the 8k resistor? Continue.