Kirchhoff's Rules and terminal voltage

[Kandycat]

Homework Statement

(a) Determine the currents I₁, I₂, I₃ in the figure. Assume the internal resistance of each batter is r = 1.0 olms

(b) What is the terminal voltage of the 6.0 V battery?

I hope you can read my handwriting.

Homework Equations

V = IR

The Attempt at a Solution

I₁ + I₂ = I₃

I don't understand kirchhoff's rules and how the internal resistance of each batter means.

 

[LowlyPion]

First the way it's drawn it's I2 + I3 = I1

All it means is that charge has to go somewhere. ∑ I_in = ∑ I_out

Direction matters.

The little r's are the internal resistances of the batteries. When they ask for the terminal V of the 6v battery they want you to include the I3*r change in voltage from 6v that you would measure in real life.

To solve you need to write out the loop equations for the 2 inner loops. Those along with your current conservation give you 3 equations and you have 3 unknown currents. So then you just solve.

 

[Kandycat]

Okay, can you tell me if my loops are right?

Top: V₁ + V₂ = I₁r + I₁R₁ + I₂r + I₂R₂ + I₁R₃

Bottom: V₃ + I₂R₂ + I₂r = I₁r + I₃r + I₃R₅ + V₂ + I₃R₄

Big: V₁ + V₃ = I₁r + I₁R₁ + I₃R₄ + I₃r + I₃R₅ + I₁R₄

 

[LowlyPion]

First of all forget the Big loop. The 2 inner loops and the conservation of current is all you need.

The top and bottom look OK just glancing at them.

Now use

I1 = I2 + I3 and you can get it down to 2 equations and 2 unknowns pretty pronto.

Then solve.

 

[Kandycat]

Okay, so I figure out the currents. I'm still pretty confused with finding terminal voltage.

Are you saying that Terminal Voltage = I₃r?

 

[LowlyPion]

Okay, so I figure out the currents. I'm still pretty confused with finding terminal voltage.

Are you saying that Terminal Voltage = I₃r?

No. Terminal voltage is 6v + I3*r. (This is if that is the right direction for I3.)