# Kirchhoff's Rules and terminal voltage

#### Kandycat

1. 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.

2. Homework Equations
V = IR

3. The Attempt at a Solution
I1 + I2 = I3

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

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#### LowlyPion

Homework Helper
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

Homework Helper
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

Homework Helper
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.)

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