# Solving Kirchoff's Rules in a DC Circuit

• hrs90
In summary: Yes, these are correct. Now, let's try to solve for V in each loop.In the left loop, V-I1R1+I2R2-V2-I1R4=0, so V= -R1+R2+R4.In the right loop, E2-I2R2-I3R3=0, so V= -R2-R3+R4.Finally, in the sum of the two loops, V= -R1+R2+R4-E2+R2-R3+R4=0, so V= -8+40+30+50=110.
hrs90

## Homework Statement

The circuit in the figure is composed of two batteries (e1 = 8 V and e2 = 6 V) and four resistors (R1 = 110 W, R2 = 40 W, R3 = 30 W, and R4 = 50 W) as shown.

[PLAIN]https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1202/fall/homework/Ch-21-DC-Circuits/kirchoff/cir06.gif

## Homework Equations

Kirchoff's Junction/Loop Rule

## The Attempt at a Solution

This problem has been giving me nightmares! I have very little understandings of these 2 rules, even though I read my book. It doesn't show clear examples. But anyway here's my poor understanding of this problem. As I understand we need to draw a loop inside the first box that increases its potential in a clockwise direction. Now its asking for the current through the first resistor, so the current I1 will pass through R1 meet the junction, split into currents I2 and I3. This is all I know. Can anyone please show what's the next step from here. And Please please make it easy for me, as I am having a really hard time with this problem. Thank you in advance!

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So far you've got: I1 goes through R1 and then splits up into I2 (going down through R2) and I3 (going right through R3). Okay, that's a good place to start.

Now what does Kirchoff's current rule say about these three currents?

Also, what is the current flowing through R4? And why?

That they all add up to zero? Also I think I1 goes through R4, but I think that I'm wrong.

hrs90 said:
That they all add up to zero?
You need to know this, not be asking us. Please get your class notes or textbook, and look up what it has for the kirchhoff current rule (or junction rule). What does it say?

Also I think I1 goes through R4, but I think that I'm wrong.
You are not wrong. But you can be sure by applying the junction rule to the lower junction.

PS: I have to leave now. Perhaps someone else will be around to help.

Goku, as I mentioned before, I did read the book and I do have my notes in front of me. And I wasn't really asking, I was just confirming, because that's what the book says about Junction Rule, all the currents at a Junction add up to zero.

Okay, good. Let's start from there.

Another way to think of the Junction Rule is this: the sum of all currents entering a junction must equal the sum of all currents leaving it.

Out of the three currents (I1, I2, I3), which ones enter and which leave the top junction?

Can you translate the words of the Junction Rule into an equation using the variables I1, I2 and I3?

Ok, I was able to finally get the 3 equations, but now I'm having problems with the algebra, this system looks really difficult to solve.

Junction Rule: I1+I2 + I3= 0
Left Loop: V-I1R1+I2R2-V2-I1R4=0
Right Loop: E2-I2R2-I3R3=0

Can you tell me if these are right, and where do i go from here? Thanks.

## 1. What are Kirchoff's Rules in a DC Circuit?

Kirchoff's Rules, also known as Kirchoff's Laws, are fundamental principles in circuit analysis that govern the behavior and flow of electric currents in a DC circuit. They are used to calculate voltage, current, and resistance in a circuit.

## 2. What is Kirchoff's first rule?

Kirchoff's first rule, also known as Kirchoff's Current Law (KCL), states that the algebraic sum of currents entering and exiting a junction in a circuit must equal zero. This means that the total current flowing into a junction must equal the total current flowing out of the junction.

## 3. What is Kirchoff's second rule?

Kirchoff's second rule, also known as Kirchoff's Voltage Law (KVL), states that the algebraic sum of voltage drops around a closed loop in a circuit must equal zero. This means that the sum of all voltage sources in a loop must be equal to the sum of all voltage drops in that same loop.

## 4. How do I apply Kirchoff's Rules in a DC circuit?

To apply Kirchoff's Rules in a DC circuit, you must first identify all the junctions and closed loops in the circuit. Then, write out the equations for KCL and KVL for each junction and loop. Finally, solve the resulting system of equations to find the unknown values in the circuit.

## 5. What are some common mistakes when solving Kirchoff's Rules in a DC circuit?

Some common mistakes when solving Kirchoff's Rules in a DC circuit include forgetting to account for the direction of current flow, not properly labeling the junctions and loops, and not properly setting up the equations for KCL and KVL. It is also important to double check your calculations and make sure all units are consistent.

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