Electric circuits, finding current with terminal voltage

[physics604]

1. What current flows through the 11.0 Ω resistor?

a) 0.21 A
b) 0.27 A
c) 0.93 A
d) 1.2 A

To summarize:

V₁ = 8.0 V
V₂ = 5.0 V
R₁ = 2.0 Ω
R₂ = 11.0 Ω
R₂ = 1.0 Ω

I know we shouldn't attach pictures, but the diagram does make the question a lot easier to understand.

Homework Equations

V=IR
V_T = ε-Ir

The Attempt at a Solution

R_T = 11.0 + 2.0 + 1.0 = 14.0 Ω
V_T = 8.0 + 5.0 = 13.0 V
I_T = V/R = 13.0/14.0 = 0.93 A.

And since current should be the same throughout a series circuit, the current through the 11.0 Ω resistor should be 0.93 too. My answer is wrong though.

Correct answer: a) 0.21 A, but I don't understand why. Please help me?

 

[barryj]

You are close but notice that the battery's oppose each other

 

[physics604]

You are close but notice that the battery's oppose each other

Yes, but what affect does that have? Does it mean the current is different in different parts of the circuit?

Am I doing the V_T and the R_T correctly?

 

[barryj]

If you write the kirchhoff voltage law around the loop, you will find that the battery voltages will subtract rather than add as you have done.

 

[physics604]

So are you saying V_T= 8.0-5.0 = 3.0 V?

But why would that happen? Kirchoff's Loops Rule just states that potential differences around a complete loop is equal to zero. Wouldn't both batteries create a positive potential change though?

 

[barryj]

Check the schematic diagram, the batteries do not add, they will subtract.