# Basic DC Circuits - Kirchoff's Rules Lab questions

• jamesrb
In summary, the author is having difficulty solving a system of equations involving currents and potential differences. He is trying to solve for i2 given the diagram of the circuit attached. He is having trouble getting everything in terms of R1,R2,R3 and ε. He is also not very comfortable working with systems of equations.
jamesrb

## Homework Statement

I need to come up with a formula to solve for i2 given the diagram of the circuit attached. I can identify 2 junctions and 3 loops.

## Homework Equations

*The algebraic sum of the currents into any junction is 0. By convention the currents entering the junction are positive and the currents leaving the junction are negative.
*The algebraic sum of the potential differences in any loop must equal 0.

Junction B: i1-i2+i3=0 (Eq.1)
Junction E: -i1+i2-i3=0 (Eq.2)
Loop ABEF: ε1-i1R1-i2R2=0 (Eq.3)
Loop BCDE: ε2-i3R3-i2R2=0 (Eq.4)
Loop ACDF: ε1-i1R1+i3R32=0 (Eq.5)

## The Attempt at a Solution

Here is where I run into trouble. I am having difficulty using the above equations to find a formula for i2. I am not sure if the equations above have an error in them or if I am heading in the wrong direction. I need to get everything in terms of R1,R2,R3 and ε. In the experiment ε1 is a fixed power supply and ε2 is a variable power supply. I am assuming we can add and subtract them and get:
ε1-1R1+i3R32=0 → -i1R1+i3R3=0
But I cannot seem to work the equations well enough to get everything in terms of Rx, i2 and ε so like I said I think there is an error above. I am also not very comfortable working with systems of equations.

#### Attachments

• Circuit2.jpg
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Have you tried using Woflram Alpha (or similar programs) to solve them? That could help you to find out if you stated the problem correctly. I can help you if you don't know how to use it.

1 person
I have used Wolfram to solve some simple systems of equations involving x and y. I am not sure where to begin with something like this.

1 person

First of all, it is important to note that there is no error in the equations provided. These are known as Kirchoff's Rules and are fundamental principles in circuit analysis.

To solve for i2, we need to use a combination of these equations. Let's start by rearranging Eq. 3 to solve for i2:

i2 = (ε1 - i1R1)/R2 (Eq. 6)

Next, let's substitute this equation into Eq. 1 and Eq. 2:

Junction B: i1 - [(ε1 - i1R1)/R2] + i3 = 0 (Eq. 7)
Junction E: -i1 + [(ε1 - i1R1)/R2] - i3 = 0 (Eq. 8)

Now, we have two equations with two unknowns (i1 and i3). We can solve these equations simultaneously to find the values of i1 and i3. Once we have these values, we can substitute them back into Eq. 6 to find the value of i2.

Alternatively, we can use a combination of Eq. 4 and Eq. 5 to solve for i2. Let's rearrange Eq. 4 to solve for i2:

i2 = (ε2 - i3R3)/R2 (Eq. 9)

Now, let's substitute this equation into Eq. 5:

ε1 - i1R1 + i3R3 - ε2 = 0 (Eq. 10)

Again, we have two equations with two unknowns (i1 and i3). We can solve these equations simultaneously to find the values of i1 and i3. Once we have these values, we can substitute them back into Eq. 9 to find the value of i2.

It is important to note that both methods should give us the same value for i2. If they do not, then there may be an error in your calculations or in the circuit itself.

I hope this helps in solving for i2. Remember, practice makes perfect when it comes to working with systems of equations in circuit analysis. Good luck!

## 1. What are Kirchoff's Rules and why are they important in DC circuits?

Kirchoff's Rules, also known as Kirchoff's Laws, are two fundamental principles in circuit analysis that help determine the voltage and current flow within a circuit. These rules are important because they provide a systematic way to analyze complex DC circuits and ensure that energy is conserved within the circuit.

## 2. What is the difference between Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL)?

Kirchoff's Current Law states that the total current entering a junction in a circuit must equal the total current leaving that junction. On the other hand, Kirchoff's Voltage Law states that the sum of all voltage drops in a closed loop circuit must equal the sum of all voltage gains in that loop.

## 3. How do you apply Kirchoff's Rules in circuit analysis?

To apply Kirchoff's Rules in circuit analysis, you first need to identify all the components in the circuit and label their values. Then, using KCL, you can write an equation at each junction point to determine the current flow. Similarly, using KVL, you can write an equation for each closed loop in the circuit to determine the voltage values.

## 4. Can Kirchoff's Rules be applied to AC circuits as well?

Yes, Kirchoff's Rules can be applied to both DC and AC circuits. However, in AC circuits, the values for voltage and current may vary over time, so the equations may need to be modified to account for this change.

## 5. What are some common mistakes when using Kirchoff's Rules in circuit analysis?

Some common mistakes when using Kirchoff's Rules include forgetting to account for the direction of current flow, not considering the polarity of voltage sources, and not properly labeling the components in the circuit. It is also important to ensure that all the junctions and loops in the circuit are accounted for in the equations.

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