# Solve Kirchhoff Problem: Find I1, I2, I3

• James.Garland
In summary, the student attempted to solve a problem involving three resistors by using Kirchhoff's current law, junction rule, and Ohm's law. However, they were not able to get the equations to work correctly.
James.Garland

## Homework Statement

Find I1, I2, I3
http://i58.tinypic.com/hwg4y0.png

(Problem included in image)

## Homework Equations

Junction Rule, Kirchhoff, Ohms Law

## The Attempt at a Solution

I don't understand Kirchhoff at all. All i got was I2=I1+I3 and I think that might be wrong.

Hi James.Garland! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

First thing: mark on each battery its positive end. You need that right, to start.

Next, what have you learned in class about starting to solve problems like this? How do you begin?

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So the positive end on the 12 V is the left and the 9 V is the right.

We haven't really done these in class at all...

What do I do to start?

James.Garland said:
We haven't really done these in class at all...

Working out for self, even part, even fail, will help you get most out of class afterwards.

Using Kirchhoff's current law, maybe this is being called junction rule, can you get a relation purely between I1, I2 and I3?

After which you can maybe use KVL and Ohm's Law and combine to set up some equations you could solve.

Okay, so at the bottom junction it looks like I1 and I3 are going in and I2 is leaving, so is the junction rule

I1+I3=I2 ?

It's handy to have a zero volt reference, so declare the junction of the 3 resistors to be zero volts. All other voltages can be measured relative to that.

You could label the junction at the top of the 20 ohms to be V volts. Now determine an expression for each current in terms of that single unknown, V.

I don't really understand but are you saying to have

V=20*I2 - 15*I1 - 30*I3 ?

James.Garland said:
Okay, so at the bottom junction it looks like I1 and I3 are going in and I2 is leaving, so is the junction rule

I1+I3=I2 ?

Yes

....

James.Garland said:
I don't really understand but are you saying to have

V=20*I2 - 15*I1 - 30*I3 ?
No. One at a time, find an expression for the current in each resistor, write it in terms of that V.

So for the next step, I think it is to write equations for the relationship between the individual loops, right?

So for the right loop, would it be

15 I1 +20 I2 = 9 Volts ?

and for the left,

20 I2 + 30 I3 = 12 Volts ?

James.Garland said:
So for the next step, I think it is to write equations for the relationship between the individual loops, right?

So for the right loop, would it be

15 I1 +20 I2 = 9 Volts ?

and for the left,

20 I2 + 30 I3 = 12 Volts ?
Yes. That's a good start. You don't need to label the V volts point I suggested, if you follow through with how you've begun.

What comes next?

I think next would be to use algebra and the three equations to solve for each, right? So,

I1 = .155
I2 = .332
I3 = .177

and this is amps, correct? Since it's current?

The units would be amps, yes. You can check that those values satisfy the equations you have, if no one else has worked out their answer for comparison.

## 1. What is Kirchhoff's circuit law?

Kirchhoff's circuit law, also known as Kirchhoff's current law and Kirchhoff's voltage law, are fundamental principles used to analyze electrical circuits. They state that the sum of currents entering and exiting a node in a circuit must be equal, and the sum of voltages around a closed loop in a circuit must also be equal.

## 2. How do you solve a Kirchhoff problem?

To solve a Kirchhoff problem, you need to set up a system of equations based on Kirchhoff's laws and the known values in the circuit. Then, you can use algebraic techniques to solve for the unknown currents. It is helpful to draw a circuit diagram and label all known values before starting the problem.

## 3. What is the difference between Kirchhoff's current law and Kirchhoff's voltage law?

Kirchhoff's current law deals with the flow of charge in a circuit, stating that the sum of currents entering and exiting a node must be equal. Kirchhoff's voltage law deals with the potential difference or voltage around a closed loop in a circuit, stating that the sum of voltages must be equal.

## 4. Can Kirchhoff's laws be applied to any type of circuit?

Yes, Kirchhoff's laws can be applied to any type of circuit, including both series and parallel circuits. They are fundamental principles that apply to all circuits, regardless of their complexity or components.

## 5. Are there any limitations to using Kirchhoff's laws to solve circuit problems?

While Kirchhoff's laws are useful in solving circuit problems, there are a few limitations to keep in mind. They assume ideal conditions, such as no resistance in wires and no energy loss in components. In reality, there is always some resistance and energy loss, which can affect the accuracy of the solutions obtained using Kirchhoff's laws.

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