Help with Kirchoff's Rules & Matrix Problems

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In summary, the conversation involves two different problems with circuits. The first problem asks for the current in each branch of a circuit with four resistors connected to a battery with a terminal voltage of 12 V. The second problem involves a matrix problem in physics, where the person is struggling with how to use their TI-83 calculator. The first problem can be solved using Kirchoff's Rules, while the second problem involves solving a system of linear equations using a matrix and Gauss elimination.
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phyznub
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urgent help on these problems!

Homework Statement



Questions 1:

http://g.imagehost.org/view/0961/DSC01830 [Broken]Kirchoff's Rules problem on resistors...?

Four resistors are connected to a battery with a terminal voltage of 12 V, as shown below. Use Kirchoff's Rules to find the current in each branch of the circuit.

Question 2:Physics Matrix problem involving circuits?I have trouble with this problem.. So i have a ti-83 so, does that mean i put it into the matrix. But then what. How do i solve the problem. Could someone give me some steps and explanation on how to do so

Thanks!

http://g.imagehost.org/view/0657/DSC01829 [Broken]

Homework Equations


I think there are the junction rule and loop rules. I1=I2+I3?
And use of calculator for matrix?

The Attempt at a Solution



1)So that would me loop and junction rule right?? how would i go about solving this problems, could someone show me the steps to do this?

2)I think I just need calculator help for this(ti-83) but what do they mean by solve it. SOlve what?
 
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  • #2


The first problem really can't be more straightforward...
You have two junctions and three loops, just write up the kirchhoff laws.

For e.g. the loop rule for the lower loop will look like: [tex]80\cdot I_2+30\cdot I_1 =12[/tex]

The junction rule is self explanatory...

The second problem is basicaly a system of linear equations. You have to solve this system of equations, i.e. find I_1, I_2 etc.

Just write the respective coefficients of the unknowns, into a matrix, and use Gauss elimination.. you don't need a calculator, since this one is quite easy
 

1. What are Kirchoff's Rules and why are they important?

Kirchoff's Rules are two principles in circuit analysis, named after German physicist Gustav Kirchoff. The first rule, Kirchoff's Current Law (KCL), states that the sum of all currents entering and exiting a junction in a circuit must be equal to zero. The second rule, Kirchoff's Voltage Law (KVL), states that the sum of all voltages around a closed loop in a circuit must be equal to zero. These rules are important because they provide a systematic method for analyzing complex circuits and can be applied to any circuit configuration.

2. How do I apply Kirchoff's Rules to a circuit problem?

To apply Kirchoff's Rules to a circuit problem, you must first draw a schematic diagram of the circuit. Then, identify all the junctions and closed loops in the circuit. Next, use KCL to write equations for the currents entering and exiting each junction. Use KVL to write equations for the voltages around each closed loop. Finally, solve the resulting system of equations to find the unknown currents and voltages in the circuit.

3. What is the difference between series and parallel circuits?

In a series circuit, the components are connected one after the other in a single path. This means that the same current flows through each component, and the total resistance of the circuit is equal to the sum of the individual resistances. In a parallel circuit, the components are connected in branches, allowing for multiple paths for the current to flow. This means that the voltage across each component is the same, and the total resistance of the circuit is less than the smallest individual resistance.

4. How do I solve a matrix problem in circuit analysis?

Matrix methods are often used to solve circuit problems with multiple unknown variables. To solve a matrix problem in circuit analysis, you must first write a set of equations based on Kirchoff's Rules. Then, these equations can be represented in matrix form, with the unknown variables as the coefficients. Use matrix operations such as row reduction to solve for the unknown variables and determine the values of currents, voltages, or resistances in the circuit.

5. Can Kirchoff's Rules be applied to AC circuits?

Yes, Kirchoff's Rules can be applied to both DC and AC circuits. However, in AC circuits, the voltages and currents are represented as complex numbers, and the equations must be solved using complex algebra. Additionally, KVL and KCL must be modified to account for the phase differences between voltages and currents in AC circuits.

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