Simultaneous Equations From Kirchhoff's Rules

In summary, the problem involves using Kirchoff's Rules to solve for three unknown currents in a lab report. The equations used are I1 + I2 = I3, I1 = (-I3R3 - V2) / (R2), and I2 = (-I3R3 + V1) / (R1). The attempt at a solution involves solving for I3 and then using the expression to plug back into the I1 and I2 equations. To solve for I3, all terms with I3 must be moved to one side of the equation and the current factored out.
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Homework Statement


For a Lab report I have to solve for three unknown currents from Kirchoff's Rules equations using simultaneous equation algebra, and I'm completely stumped.

Homework Equations



From Loop and junction equations, the three equations that I have are

I1 + I2 = I3

I1= (-I3R3 - V2)/ (R2)

I2= (-I3R3+V1)/(R1)

The Attempt at a Solution



This is the farthest I have gotten, solving for I3. Once I have expression for this I will be able to plug back into the I1 and I2 equations fairly easy.

(-I3R3R2+ -I3R3R1+ -V2R1) / (R1R2)

= I3R1R2

Sorry If this is confusing. Thanks for any help in advance.
 
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  • #2
You should just have to move all the terms with I3 to one side of the equation and factor out the current. That should give you an answer for I3.
 

FAQ: Simultaneous Equations From Kirchhoff's Rules

1. What are Kirchhoff's Rules?

Kirchhoff's Rules, also known as Kirchhoff's Laws, are fundamental principles in circuit analysis that help determine the voltage and current distribution in an electrical circuit. These rules are based on the principles of conservation of charge and energy.

2. What is a simultaneous equation in the context of Kirchhoff's Rules?

A simultaneous equation in the context of Kirchhoff's Rules refers to the equations that are used to solve for the unknown currents and voltages in a circuit. These equations are derived from applying Kirchhoff's Laws to the different nodes and loops in a circuit.

3. How do you use Kirchhoff's Rules to solve for simultaneous equations?

To solve for simultaneous equations using Kirchhoff's Rules, you first need to identify all the nodes and loops in the circuit. Then, apply Kirchhoff's Current Law (KCL) at each node and Kirchhoff's Voltage Law (KVL) along each loop. This will result in a set of equations that can be solved simultaneously to find the values of the unknown variables.

4. Can Kirchhoff's Rules be applied to any circuit?

Yes, Kirchhoff's Rules can be applied to any circuit, whether it is a simple series or parallel circuit, or a more complex circuit with multiple nodes and loops. These rules are based on fundamental principles of physics and are applicable to all electrical circuits.

5. What are some real-world applications of simultaneous equations from Kirchhoff's Rules?

Simultaneous equations from Kirchhoff's Rules are commonly used in the design and analysis of electrical circuits, such as in electronic devices, power systems, and communication networks. They are also used in the fields of physics and engineering to model and solve complex systems involving multiple variables and equations.

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