# Using Kirchhoff's laws to find current in a circuit

• Engineering
• november1992
In summary, the circuit can be solved using both KCL and KVL. The KVL solution for I1 is 1.5A, while the KCL solution yields a system of equations with 3 unknowns. By adding a 3rd KCL equation at the node between the 8 ohm and 4 ohm resistor, the solution for I1 is confirmed to be 2A.
november1992

## Homework Statement

Use KCL and KVL to determine the currents I1 to I3 in the circuit below:

## Homework Equations

Ʃ$v_{n}$ = 0
Ʃ$i_{n}$ = 0
v=ir

## The Attempt at a Solution

I got two different answers for $I_{1}$ using the two different laws. I'm not sure if I'm doing it right.

KVL @ loop 1: -18 + 6 + 8$I_{1}$ = 0
8 $I_{1}$ = 12
$I_{1}$ = 1.5AKCL @ node a: 3 = $I_{1}$ + $I_{2}$ + 1
KCL @ node b: $I_{3}$ = 1 + $I_{2}$
0 = $I_{1}$ + $I_{2}$ -2
0 = -1 - $I_{2}$ + $I_{3}$
1 = $I_{3}$
0 = $I_{2}$
2 = $I_{1}$

november1992 said:

## Homework Statement

Use KCL and KVL to determine the currents I1 to I3 in the circuit below:

## Homework Equations

Ʃ$v_{n}$ = 0
Ʃ$i_{n}$ = 0
v=ir

## The Attempt at a Solution

I got two different answers for $I_{1}$ using the two different laws. I'm not sure if I'm doing it right.

KVL @ loop 1: -18 + 6 + 8$I_{1}$ = 0
8 $I_{1}$ = 12
$I_{1}$ = 1.5A

KCL @ node a: 3 = $I_{1}$ + $I_{2}$ + 1
KCL @ node b: $I_{3}$ = 1 + $I_{2}$

0 = $I_{1}$ + $I_{2}$ -2
0 = -1 - $I_{2}$ + $I_{3}$
1 = $I_{3}$
0 = $I_{2}$
2 = $I_{1}$

Your KVL solution for I1 is correct. For the KCL solution, you have 3 unknowns but you have only written 2 equations. That isn't sufficient to solve for I1 yet...

Could I substitute the value that I got for I1 from the KVL equation into KCL?
I wasn't sure if I could do that because I thought the question was asking me to find the values separately using the two different laws.

november1992 said:
Could I substitute the value that I got for I1 from the KVL equation into KCL?
I wasn't sure if I could do that because I thought the question was asking me to find the values separately using the two different laws.

It does sound like they want you to solve the circuit with each technique separately. It's a pretty easy circuit to solve by inspection anyway, so they must want you to go through all the steps of each technique separately for practice.

So can you see another node where you could write a 3rd KCL equation?

The one between the 8 ohm and 4 ohm resistor?

november1992 said:
The one between the 8 ohm and 4 ohm resistor?

That might work...

nvm I figured it out, thanks for the help.

Last edited:

## 1. What are Kirchhoff's laws?

Kirchhoff's laws are two fundamental principles in circuit analysis that govern the behavior of electric currents and voltages in a closed circuit. The first law, also known as Kirchhoff's current law (KCL), states that the algebraic sum of currents entering and leaving a node in a circuit must equal zero. The second law, also known as Kirchhoff's voltage law (KVL), states that the sum of voltages around any closed loop in a circuit must equal zero.

## 2. How do I use Kirchhoff's laws to find the current in a circuit?

To use Kirchhoff's laws to find the current in a circuit, you must first identify the nodes and loops in the circuit. Then, apply KCL to each node to determine the current entering and leaving the node. Next, apply KVL to each loop to determine the sum of voltages around the loop. Finally, use Ohm's law (V=IR) to calculate the current at any desired point in the circuit.

## 3. Can Kirchhoff's laws be used in any type of circuit?

Yes, Kirchhoff's laws can be used in any type of circuit, including parallel and series circuits. They are fundamental principles that apply to all types of circuits and are essential for circuit analysis and design.

## 4. What are some common mistakes to avoid when using Kirchhoff's laws?

Some common mistakes to avoid when using Kirchhoff's laws include incorrectly labeling nodes and loops, not properly accounting for the direction of current flow, and neglecting to consider the polarity of voltage sources in KVL. It is important to be thorough and attentive when applying these laws to ensure accurate results.

## 5. Are there any alternative methods for finding current in a circuit?

Yes, there are alternative methods for finding current in a circuit, such as using nodal analysis or mesh analysis. However, Kirchhoff's laws are often the preferred method as they are simple and applicable to all types of circuits. It is always beneficial to have a solid understanding of these laws and how to use them for circuit analysis.

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