Kirchhoff's law - Simultanious Equations - Question

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In summary, Kirchhoff's laws can be applied to solve for the current I^1 and I^2 in a specific electrical circuit. The equations 27 = 1.5 I^1 + 8 (I^1 - I^2) and -26 = 2 I^2 - 8 (I^1 - I^2) can be used to find the values of I^1 and I^2 by setting I^1 = x and I^2 = y and solving for x and y. This can be done by eliminating y from the two equations through basic algebra. The specific steps for solving the equations are not provided, but it is assumed that the reader is capable of doing the algebraic work
  • #1
College_Noobie
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When Kirchhoff's law are applied to a particular electrical circuit the current I^1 & I^2 are connected by the equations;

27 = 1.5 I^1 + 8 (I^1 - I^2)
-26 = 2 I^2 - 8 (I^1 - I^2)

Please show working out =)
 
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  • #2
Why was this posted under "differential equations"?

Taking I^1= x and I^2= y because your notation was confusing me, you have
27= 1.5x+ 8(x-y)= 1.5x+ 8x- 8y= 9.5x- 8y and
-26= 2y- 8(x- y)= 2y- 8x+ 8y= 10y- 8x.

That is you want to solve the equations 8x- 10y= 26 and 9.5x- 8y= 27.

You might try multiplying the first equation by 4 (so you get -40y) and the second equation by -5 (so you get +40y) and adding those equations to eliminate y.

No, I'm not going to "show working out". I am going to assume that you are capable of doing the basic algebra here yourself! The practice will do you good.
 
  • #3
sorry about the place of posting i was unable to work out which of the mathimatics sections it should go under.

and sorry about the "I to the power of 1 and I to the power of 2"

dont worry about the working out =) i will be able to carry on from there

Thanks
 

1. What is Kirchhoff's law?

Kirchhoff's law, also known as Kirchhoff's circuit laws, are two fundamental principles in circuit analysis that relate to the conservation of energy and charge. They are used to determine the behavior of electric circuits and are essential in understanding and designing electronic devices.

2. What are Kirchhoff's circuit laws?

Kirchhoff's circuit laws consist of two laws: Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). KCL states that the sum of currents entering a node in a circuit must equal the sum of currents leaving the node. KVL states that the sum of voltages around a closed loop in a circuit must equal zero.

3. How do Kirchhoff's laws relate to simultaneous equations?

In order to solve a circuit using Kirchhoff's laws, we often need to create a system of simultaneous equations. These equations are formed by applying KCL and KVL to different parts of the circuit. By solving these equations, we can determine the values of currents and voltages at different points in the circuit.

4. What are some applications of Kirchhoff's laws?

Kirchhoff's laws have a wide range of applications in circuit analysis and design. They are used in the design of electronic devices such as computers, televisions, and cell phones. They are also used in power systems to ensure proper distribution of electricity. In addition, they are used in physics and engineering courses to teach principles of circuit analysis.

5. Are there any limitations to Kirchhoff's laws?

While Kirchhoff's laws are essential in circuit analysis, there are some limitations to their application. These laws assume ideal conditions, such as no resistance in wires and no magnetic fields, which may not be true in real-life circuits. Additionally, these laws only work for linear circuits, meaning that the relationship between current and voltage must be linear. Nonlinear circuits may require more complex methods of analysis.

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